diff --git a/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueStore.java b/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueStore.java
index 4c66696e3c8..3c6b91ec018 100644
--- a/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueStore.java
+++ b/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueStore.java
@@ -375,7 +375,8 @@ public long getOffsetInQueueByTime(String topic, int queueId, long timestamp, Bo
         if (high == null || high == -1) {
             return 0;
         }
-        return this.rocksDBConsumeQueueTable.binarySearchInCQByTime(topic, queueId, high, low, timestamp, minPhysicOffset);
+        return this.rocksDBConsumeQueueTable.binarySearchInCQByTime(topic, queueId, high, low, timestamp,
+            minPhysicOffset, boundaryType);
     }
 
     @Override
diff --git a/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueTable.java b/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueTable.java
index 0a735ea27c1..c7d35fa8c0c 100644
--- a/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueTable.java
+++ b/store/src/main/java/org/apache/rocketmq/store/queue/RocksDBConsumeQueueTable.java
@@ -20,6 +20,7 @@
 import java.util.ArrayList;
 import java.util.List;
 
+import org.apache.rocketmq.common.BoundaryType;
 import org.apache.rocketmq.common.Pair;
 import org.apache.rocketmq.common.constant.LoggerName;
 import org.apache.rocketmq.logging.org.slf4j.Logger;
@@ -180,10 +181,10 @@ public void destroyCQ(final String topic, final int queueId, WriteBatch writeBat
     }
 
     public long binarySearchInCQByTime(String topic, int queueId, long high, long low, long timestamp,
-        long minPhysicOffset) throws RocksDBException {
-        long result = 0;
+        long minPhysicOffset, BoundaryType boundaryType) throws RocksDBException {
+        long result = -1L;
         long targetOffset = -1L, leftOffset = -1L, rightOffset = -1L;
-        long leftValue = -1L, rightValue = -1L;
+        long ceiling = high, floor = low;
         while (high >= low) {
             long midOffset = low + ((high - low) >>> 1);
             ByteBuffer byteBuffer = getCQInKV(topic, queueId, midOffset);
@@ -209,22 +210,64 @@ public long binarySearchInCQByTime(String topic, int queueId, long high, long lo
             } else if (storeTime > timestamp) {
                 high = midOffset - 1;
                 rightOffset = midOffset;
-                rightValue = storeTime;
             } else {
                 low = midOffset + 1;
                 leftOffset = midOffset;
-                leftValue = storeTime;
             }
         }
         if (targetOffset != -1) {
+            // offset next to it might also share the same store-timestamp.
+            switch (boundaryType) {
+                case LOWER: {
+                    while (true) {
+                        long nextOffset = targetOffset - 1;
+                        if (nextOffset < floor) {
+                            break;
+                        }
+                        ByteBuffer byteBuffer = getCQInKV(topic, queueId, nextOffset);
+                        long storeTime = byteBuffer.getLong(MSG_STORE_TIME_SIZE_OFFSET);
+                        if (storeTime != timestamp) {
+                            break;
+                        }
+                        targetOffset = nextOffset;
+                    }
+                    break;
+                }
+                case UPPER: {
+                    while (true) {
+                        long nextOffset = targetOffset + 1;
+                        if (nextOffset > ceiling) {
+                            break;
+                        }
+                        ByteBuffer byteBuffer = getCQInKV(topic, queueId, nextOffset);
+                        long storeTime = byteBuffer.getLong(MSG_STORE_TIME_SIZE_OFFSET);
+                        if (storeTime != timestamp) {
+                            break;
+                        }
+                        targetOffset = nextOffset;
+                    }
+                    break;
+                }
+                default: {
+                    log.warn("Unknown boundary type");
+                    break;
+                }
+            }
             result = targetOffset;
         } else {
-            if (leftValue == -1) {
-                result = rightOffset;
-            } else if (rightValue == -1) {
-                result = leftOffset;
-            } else {
-                result = Math.abs(timestamp - leftValue) > Math.abs(timestamp - rightValue) ? rightOffset : leftOffset;
+            switch (boundaryType) {
+                case LOWER: {
+                    result = rightOffset;
+                    break;
+                }
+                case UPPER: {
+                    result = leftOffset;
+                    break;
+                }
+                default: {
+                    log.warn("Unknown boundary type");
+                    break;
+                }
             }
         }
         return result;