diff --git a/spring-beans/src/main/java/org/springframework/beans/PropertyEditorRegistrySupport.java b/spring-beans/src/main/java/org/springframework/beans/PropertyEditorRegistrySupport.java
index da6b9232919..fcde6786e0b 100644
--- a/spring-beans/src/main/java/org/springframework/beans/PropertyEditorRegistrySupport.java
+++ b/spring-beans/src/main/java/org/springframework/beans/PropertyEditorRegistrySupport.java
@@ -79,12 +79,15 @@ import org.springframework.util.ClassUtils;
 
 /**
  * Base implementation of the {@link PropertyEditorRegistry} interface.
- * Provides management of default editors and custom editors.
- * Mainly serves as base class for {@link BeanWrapperImpl}.
+ *
+ * <p>Provides management of default editors and custom editors.
+ *
+ * <p>Mainly serves as base class for {@link BeanWrapperImpl}.
  *
  * @author Juergen Hoeller
  * @author Rob Harrop
  * @author Sebastien Deleuze
+ * @author Sam Brannen
  * @since 1.2.6
  * @see java.beans.PropertyEditorManager
  * @see java.beans.PropertyEditorSupport#setAsText
@@ -92,6 +95,15 @@ import org.springframework.util.ClassUtils;
  */
 public class PropertyEditorRegistrySupport implements PropertyEditorRegistry {
 
+	/**
+	 * The maximum number of {@code [key]} segments that {@link #addStrippedPropertyPaths}
+	 * will process in a single property path, to avoid excessive recursion and the
+	 * resulting exponential blowup in the number of generated stripped paths for
+	 * property paths with a large number of {@code [key]} segments.
+	 * @since 7.1
+	 */
+	private static final int MAX_STRIPPED_PROPERTY_PATH_DEPTH = 8;
+
 	private @Nullable ConversionService conversionService;
 
 	private boolean defaultEditorsActive = false;
@@ -500,12 +512,23 @@ public class PropertyEditorRegistrySupport implements PropertyEditorRegistry {
 
 	/**
 	 * Add property paths with all variations of stripped keys and/or indexes.
-	 * Invokes itself recursively with nested paths.
+	 * <p>Invokes itself recursively with nested paths, bounded to a nesting depth
+	 * of {@link #MAX_STRIPPED_PROPERTY_PATH_DEPTH}.
 	 * @param strippedPaths the result list to add to
 	 * @param nestedPath the current nested path
 	 * @param propertyPath the property path to check for keys/indexes to strip
 	 */
 	private void addStrippedPropertyPaths(List<String> strippedPaths, String nestedPath, String propertyPath) {
+		addStrippedPropertyPaths(strippedPaths, nestedPath, propertyPath, 0);
+	}
+
+	private void addStrippedPropertyPaths(
+			List<String> strippedPaths, String nestedPath, String propertyPath, int depth) {
+
+		if (depth >= MAX_STRIPPED_PROPERTY_PATH_DEPTH) {
+			// Avoid excessive recursion.
+			return;
+		}
 		int startIndex = propertyPath.indexOf(PropertyAccessor.PROPERTY_KEY_PREFIX_CHAR);
 		if (startIndex != -1) {
 			int endIndex = propertyPath.indexOf(PropertyAccessor.PROPERTY_KEY_SUFFIX_CHAR);
@@ -516,9 +539,9 @@ public class PropertyEditorRegistrySupport implements PropertyEditorRegistry {
 				// Strip the first key.
 				strippedPaths.add(nestedPath + prefix + suffix);
 				// Search for further keys to strip, with the first key stripped.
-				addStrippedPropertyPaths(strippedPaths, nestedPath + prefix, suffix);
+				addStrippedPropertyPaths(strippedPaths, nestedPath + prefix, suffix, depth + 1);
 				// Search for further keys to strip, with the first key not stripped.
-				addStrippedPropertyPaths(strippedPaths, nestedPath + prefix + key, suffix);
+				addStrippedPropertyPaths(strippedPaths, nestedPath + prefix + key, suffix, depth + 1);
 			}
 		}
 	}
diff --git a/spring-beans/src/test/java/org/springframework/beans/PropertyEditorRegistrySupportTests.java b/spring-beans/src/test/java/org/springframework/beans/PropertyEditorRegistrySupportTests.java
new file mode 100644
index 00000000000..b596934ac43
--- /dev/null
+++ b/spring-beans/src/test/java/org/springframework/beans/PropertyEditorRegistrySupportTests.java
@@ -0,0 +1,93 @@
+/*
+ * Copyright 2002-present the original author or authors.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      https://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.springframework.beans;
+
+import java.beans.PropertyEditor;
+
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.api.Timeout;
+
+import org.springframework.beans.propertyeditors.CustomNumberEditor;
+
+import static org.assertj.core.api.Assertions.assertThat;
+
+/**
+ * Tests for {@link PropertyEditorRegistrySupport}.
+ *
+ * @author Sam Brannen
+ * @since 7.1
+ */
+class PropertyEditorRegistrySupportTests {
+
+	/**
+	 * Matches the private {@code MAX_STRIPPED_PROPERTY_PATH_DEPTH} constant in
+	 * {@link PropertyEditorRegistrySupport}.
+	 */
+	private static final int MAX_DEPTH = 8;
+
+	private final PropertyEditorRegistrySupport registry = new PropertyEditorRegistrySupport();
+
+	private final PropertyEditor editor = new CustomNumberEditor(Integer.class, true);
+
+
+	@Test
+	void findCustomEditorMatchesStrippedPathAtMaxSupportedNestingDepth() {
+		registry.registerCustomEditor(null, "list", this.editor);
+
+		String propertyPath = "list" + "[0]".repeat(MAX_DEPTH);
+		assertThat(registry.findCustomEditor(null, propertyPath)).isSameAs(this.editor);
+	}
+
+	@Test
+	void findCustomEditorDoesNotMatchStrippedPathBeyondMaxSupportedNestingDepth() {
+		registry.registerCustomEditor(null, "list", this.editor);
+
+		String propertyPath = "list" + "[0]".repeat(MAX_DEPTH + 1);
+		assertThat(registry.findCustomEditor(null, propertyPath)).isNull();
+	}
+
+	@Test  // gh-37020
+	@Timeout(5)
+	void findCustomEditorWithExcessivelyNestedPropertyPathDoesNotHang() {
+		registry.registerCustomEditor(null, "attrs", this.editor);
+
+		// A property path with a bracket-nesting depth (40) that would previously
+		// have caused addStrippedPropertyPaths() to recursively enumerate 2^40 - 1
+		// stripped path variants. With the depth limit in place, this should return
+		// promptly.
+		String propertyPath = "attrs" + "[k]".repeat(40);
+
+		assertThat(registry.findCustomEditor(null, propertyPath)).isNull();
+	}
+
+	@Test
+	void guessPropertyTypeFromEditorsMatchesStrippedPathAtMaxSupportedNestingDepth() {
+		registry.registerCustomEditor(Integer.class, "list", this.editor);
+
+		String propertyPath = "list" + "[0]".repeat(MAX_DEPTH);
+		assertThat(registry.guessPropertyTypeFromEditors(propertyPath)).isEqualTo(Integer.class);
+	}
+
+	@Test
+	void guessPropertyTypeFromEditorsDoesNotMatchStrippedPathBeyondMaxSupportedNestingDepth() {
+		registry.registerCustomEditor(Integer.class, "list", this.editor);
+
+		String propertyPath = "list" + "[0]".repeat(MAX_DEPTH + 1);
+		assertThat(registry.guessPropertyTypeFromEditors(propertyPath)).isNull();
+	}
+
+}