diff --git a/tony-core/src/main/java/com/linkedin/tony/TonyConfigurationKeys.java b/tony-core/src/main/java/com/linkedin/tony/TonyConfigurationKeys.java
index fbe7cd8e..3a0ba311 100644
--- a/tony-core/src/main/java/com/linkedin/tony/TonyConfigurationKeys.java
+++ b/tony-core/src/main/java/com/linkedin/tony/TonyConfigurationKeys.java
@@ -345,6 +345,8 @@ public static String getContainerDockerMountKey() {
   public static final String GROUP_REGEX = TONY_APPLICATION_PREFIX + "group\\.([A-Za-z]+)$";
   public static final String GROUP_DEPEND_TIMEOUT_REGEX =
       TONY_APPLICATION_PREFIX + "dependency\\.([A-Za-z]+)\\.timeout\\.after\\.([A-Za-z]+)$";
+  public static final String GROUP_DEPEND_TIMEOUT_IGNORE_REGEX =
+          TONY_APPLICATION_PREFIX + "dependency\\.([A-Za-z]+)\\.timeout\\.after\\.([A-Za-z]+)$.ignored";
 
   public static String getGroupKey(String groupName) {
     return String.format(TONY_APPLICATION_PREFIX + "group.%s", groupName);
@@ -353,4 +355,8 @@ public static String getGroupKey(String groupName) {
   public static String getGroupDependentKey(String grp, String dependentGrp) {
     return String.format(TONY_APPLICATION_PREFIX + "dependency.%s.timeout.after.%s", grp, dependentGrp);
   }
+
+  public static String getGroupDependentIgnoredKey(String roleType, String dependentGrp) {
+    return String.format(TONY_APPLICATION_PREFIX + "dependency.%s.timeout.after.%s.ignored", roleType, dependentGrp);
+  }
 }
diff --git a/tony-core/src/main/java/com/linkedin/tony/runtime/MLGenericRuntime.java b/tony-core/src/main/java/com/linkedin/tony/runtime/MLGenericRuntime.java
index ee5e1765..5c1928bd 100644
--- a/tony-core/src/main/java/com/linkedin/tony/runtime/MLGenericRuntime.java
+++ b/tony-core/src/main/java/com/linkedin/tony/runtime/MLGenericRuntime.java
@@ -41,6 +41,7 @@
 import com.linkedin.tony.util.Utils;
 
 import static com.linkedin.tony.Constants.SIDECAR_TB_ROLE_NAME;
+import static com.linkedin.tony.TonyConfigurationKeys.getGroupDependentIgnoredKey;
 
 public abstract class MLGenericRuntime implements FrameworkRuntime {
     private static final long REGISTRATION_STATUS_INTERVAL_MS = 15 * 1000;
@@ -137,9 +138,16 @@ public boolean isHealthy(Configuration tonyConf) {
          * chief/workers are finished, the mechanism of dependency group timeout will make job failed.
          *
          * Dependency group timeout configuration as follows:
-         *
+         * ```
          * tony.application.group.A = worker,chief
          * tony.application.dependency.evaluator.timeout.after.A = 3600
+         * ```
+         *
+         * And in some of the cases, we don't want to fail the whole job even though a dependency times out.
+         * For example, if chief succeeded and there is a worker hanging for 1 hour,
+         * users can configure the job to still pass. So it introduces the new config of
+         * `tony.application.dependency.[X].timeout.after.[GROUP].ignored = true`, and more details could be
+         * found in https://github.com/tony-framework/TonY/issues/641.
          *
          */
         String errorMsg = null;
@@ -231,10 +239,19 @@ protected String groupDependencyTimeout(Configuration tonyConf) {
             log.info("Running job type: " + runningTaskType + ", all dependent task finished: " + allDependentTaskFinished);
 
             if (System.currentTimeMillis() - latestEndTimeInAllDependentTasks > timeout) {
-                return String.format("Jobtype: %s runs exceeded timeout(%s sec) because it's "
-                                + "dependent group: %s (task set: [%s]) has been finished",
-                        runningTaskType, dependentGroupPair.getValue(), dependentGroupName,
-                        StringUtils.join(grpWithMembersIndex.get(dependentGroupName), ","));
+                String ignoredTaskTypeKey = getGroupDependentIgnoredKey(runningTaskType, dependentGroupName);
+                boolean ignoreTimeout = tonyConf.getBoolean(ignoredTaskTypeKey, false);
+                if (!ignoreTimeout) {
+                    return String.format("Task type: %s runs exceeded timeout because it's "
+                                    + "dependent group: %s (task set: [%s]) has been finished.",
+                            runningTaskType, dependentGroupName,
+                            StringUtils.join(grpWithMembersIndex.get(dependentGroupName), ","));
+                }
+
+                log.info(
+                        String.format("Task type: %s is marked as untracked.", runningJobTypes)
+                );
+                session.makeTaskTypeUntracked(runningTaskType);
             }
         }
 
diff --git a/tony-core/src/main/java/com/linkedin/tony/tensorflow/TonySession.java b/tony-core/src/main/java/com/linkedin/tony/tensorflow/TonySession.java
index 2d2eb1d3..78f56074 100644
--- a/tony-core/src/main/java/com/linkedin/tony/tensorflow/TonySession.java
+++ b/tony-core/src/main/java/com/linkedin/tony/tensorflow/TonySession.java
@@ -22,6 +22,7 @@
 import java.util.concurrent.ConcurrentHashMap;
 import java.util.stream.Collectors;
 
+import org.apache.commons.lang3.StringUtils;
 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
 import org.apache.hadoop.conf.Configuration;
@@ -39,6 +40,8 @@
 
 import static com.linkedin.tony.Constants.CHIEF_JOB_NAME;
 import static com.linkedin.tony.Constants.WORKER_JOB_NAME;
+import static com.linkedin.tony.TonyConfigurationKeys.UNTRACKED_JOBTYPES;
+import static com.linkedin.tony.util.Utils.getUntrackedJobTypes;
 
 
 /**
@@ -639,4 +642,11 @@ public int getNumRegisteredTasks() {
   public Set<String> getRegisteredTasks() {
     return registeredTasks;
   }
+
+  public void makeTaskTypeUntracked(String taskType) {
+    String[] defaultUntrackedTypes = getUntrackedJobTypes(tonyConf);
+    List<String> untrackedList = Arrays.stream(defaultUntrackedTypes).collect(Collectors.toList());
+    untrackedList.add(taskType);
+    tonyConf.set(UNTRACKED_JOBTYPES, StringUtils.join(untrackedList, ","));
+  }
 }