diff --git a/spring-boot-project/spring-boot-docker-compose/src/main/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironment.java b/spring-boot-project/spring-boot-docker-compose/src/main/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironment.java
index 4a63bbc0b68b..7858bdba5c46 100644
--- a/spring-boot-project/spring-boot-docker-compose/src/main/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironment.java
+++ b/spring-boot-project/spring-boot-docker-compose/src/main/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironment.java
@@ -28,6 +28,7 @@
  * @author Andy Wilkinson
  * @author Phillip Webb
  * @author Scott Frederick
+ * @author Sidmar Theodoro
  */
 class PostgresEnvironment {
 
@@ -44,11 +45,19 @@ class PostgresEnvironment {
 	}
 
 	private String extractPassword(Map<String, String> env) {
+		if (hasTrustAuthMethod(env)) {
+			return null;
+		}
 		String password = env.getOrDefault("POSTGRES_PASSWORD", env.get("POSTGRESQL_PASSWORD"));
 		Assert.state(StringUtils.hasLength(password), "PostgreSQL password must be provided");
 		return password;
 	}
 
+	private Boolean hasTrustAuthMethod(Map<String, String> env) {
+		String hostAuthMethod = env.get("POSTGRES_HOST_AUTH_METHOD");
+		return "trust".equals(hostAuthMethod);
+	}
+
 	String getUsername() {
 		return this.username;
 	}
diff --git a/spring-boot-project/spring-boot-docker-compose/src/test/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironmentTests.java b/spring-boot-project/spring-boot-docker-compose/src/test/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironmentTests.java
index 9058c1f11d70..0bd2c4b1cb7e 100644
--- a/spring-boot-project/spring-boot-docker-compose/src/test/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironmentTests.java
+++ b/spring-boot-project/spring-boot-docker-compose/src/test/java/org/springframework/boot/docker/compose/service/connection/postgres/PostgresEnvironmentTests.java
@@ -78,6 +78,12 @@ void getPasswordWhenHasPostgresqlPassword() {
 		assertThat(environment.getPassword()).isEqualTo("secret");
 	}
 
+	@Test
+	void getPasswordWhenHasTrustHostAuthMethod() {
+		PostgresEnvironment environment = new PostgresEnvironment(Map.of("POSTGRES_HOST_AUTH_METHOD", "trust"));
+		assertThat(environment.getPassword()).isNull();
+	}
+
 	@Test
 	void getDatabaseWhenNoPostgresDbOrPostgresUser() {
 		PostgresEnvironment environment = new PostgresEnvironment(Map.of("POSTGRES_PASSWORD", "secret"));