diff --git a/core/src/main/scala/org/apache/spark/memory/UnifiedMemoryManager.scala b/core/src/main/scala/org/apache/spark/memory/UnifiedMemoryManager.scala
index fea2808218a53..df193552bed3c 100644
--- a/core/src/main/scala/org/apache/spark/memory/UnifiedMemoryManager.scala
+++ b/core/src/main/scala/org/apache/spark/memory/UnifiedMemoryManager.scala
@@ -160,7 +160,7 @@ private[spark] class UnifiedMemoryManager private[memory] (
       case MemoryMode.OFF_HEAP => (
         offHeapExecutionMemoryPool,
         offHeapStorageMemoryPool,
-        maxOffHeapMemory)
+        maxOffHeapStorageMemory)
     }
     if (numBytes > maxMemory) {
       // Fail fast if the block simply won't fit
@@ -171,7 +171,8 @@ private[spark] class UnifiedMemoryManager private[memory] (
     if (numBytes > storagePool.memoryFree) {
       // There is not enough free memory in the storage pool, so try to borrow free memory from
       // the execution pool.
-      val memoryBorrowedFromExecution = Math.min(executionPool.memoryFree, numBytes)
+      val memoryBorrowedFromExecution = Math.min(executionPool.memoryFree,
+        numBytes - storagePool.memoryFree)
       executionPool.decrementPoolSize(memoryBorrowedFromExecution)
       storagePool.incrementPoolSize(memoryBorrowedFromExecution)
     }
diff --git a/core/src/test/scala/org/apache/spark/memory/MemoryManagerSuite.scala b/core/src/test/scala/org/apache/spark/memory/MemoryManagerSuite.scala
index eb2b3ffd1509a..85eeb5055ae03 100644
--- a/core/src/test/scala/org/apache/spark/memory/MemoryManagerSuite.scala
+++ b/core/src/test/scala/org/apache/spark/memory/MemoryManagerSuite.scala
@@ -117,7 +117,7 @@ private[memory] trait MemoryManagerSuite extends SparkFunSuite with BeforeAndAft
         evictBlocksToFreeSpaceCalled.set(numBytesToFree)
         if (numBytesToFree <= mm.storageMemoryUsed) {
           // We can evict enough blocks to fulfill the request for space
-          mm.releaseStorageMemory(numBytesToFree, MemoryMode.ON_HEAP)
+          mm.releaseStorageMemory(numBytesToFree, mm.tungstenMemoryMode)
           evictedBlocks += Tuple2(null, BlockStatus(StorageLevel.MEMORY_ONLY, numBytesToFree, 0L))
           numBytesToFree
         } else {
diff --git a/core/src/test/scala/org/apache/spark/memory/UnifiedMemoryManagerSuite.scala b/core/src/test/scala/org/apache/spark/memory/UnifiedMemoryManagerSuite.scala
index c821054412d7d..02b04cdbb2a5f 100644
--- a/core/src/test/scala/org/apache/spark/memory/UnifiedMemoryManagerSuite.scala
+++ b/core/src/test/scala/org/apache/spark/memory/UnifiedMemoryManagerSuite.scala
@@ -303,4 +303,36 @@ class UnifiedMemoryManagerSuite extends MemoryManagerSuite with PrivateMethodTes
     mm.invokePrivate[Unit](assertInvariants())
   }
 
+  test("not enough free memory in the storage pool --OFF_HEAP") {
+    val conf = new SparkConf()
+      .set("spark.memory.offHeap.size", "1000")
+      .set("spark.testing.memory", "1000")
+      .set("spark.memory.offHeap.enabled", "true")
+    val taskAttemptId = 0L
+    val mm = UnifiedMemoryManager(conf, numCores = 1)
+    val ms = makeMemoryStore(mm)
+    val memoryMode = MemoryMode.OFF_HEAP
+
+    assert(mm.acquireExecutionMemory(400L, taskAttemptId, memoryMode) === 400L)
+    assert(mm.storageMemoryUsed === 0L)
+    assert(mm.executionMemoryUsed === 400L)
+
+    // Fail fast
+    assert(!mm.acquireStorageMemory(dummyBlock, 700L, memoryMode))
+    assert(mm.storageMemoryUsed === 0L)
+
+    assert(mm.acquireStorageMemory(dummyBlock, 100L, memoryMode))
+    assert(mm.storageMemoryUsed === 100L)
+    assertEvictBlocksToFreeSpaceNotCalled(ms)
+
+    // Borrow 50 from execution memory
+    assert(mm.acquireStorageMemory(dummyBlock, 450L, memoryMode))
+    assertEvictBlocksToFreeSpaceNotCalled(ms)
+    assert(mm.storageMemoryUsed === 550L)
+
+    // Borrow 50 from execution memory and evict 50 to free space
+    assert(mm.acquireStorageMemory(dummyBlock, 100L, memoryMode))
+    assertEvictBlocksToFreeSpaceCalled(ms, 50)
+    assert(mm.storageMemoryUsed === 600L)
+  }
 }