diff --git a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/FileSourceStrategy.scala b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/FileSourceStrategy.scala
index 16b22717b8d9..e55a0f5ab761 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/FileSourceStrategy.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/FileSourceStrategy.scala
@@ -22,7 +22,7 @@ import org.apache.spark.sql._
 import org.apache.spark.sql.catalyst.expressions
 import org.apache.spark.sql.catalyst.expressions._
 import org.apache.spark.sql.catalyst.planning.PhysicalOperation
-import org.apache.spark.sql.catalyst.plans.logical.LogicalPlan
+import org.apache.spark.sql.catalyst.plans.logical.{LogicalPlan, Project}
 import org.apache.spark.sql.execution.FileSourceScanExec
 import org.apache.spark.sql.execution.SparkPlan
 
@@ -51,6 +51,15 @@ import org.apache.spark.sql.execution.SparkPlan
  */
 object FileSourceStrategy extends Strategy with Logging {
   def apply(plan: LogicalPlan): Seq[SparkPlan] = plan match {
+    case p @ Project(fields, child)
+      if !fields.forall(_.deterministic) && p.references.nonEmpty =>
+      collectFileSource(Project(child.output.filter(p.references.contains), child))
+        .map(p => execution.ProjectExec(fields, p)).toList
+
+    case _ => collectFileSource(plan)
+  }
+
+  private def collectFileSource(plan: LogicalPlan): Seq[SparkPlan] = plan match {
     case PhysicalOperation(projects, filters,
       l @ LogicalRelation(fsRelation: HadoopFsRelation, _, table, _)) =>
       // Filters on this relation fall into four categories based on where we can use them to avoid
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/DataFrameSuite.scala b/sql/core/src/test/scala/org/apache/spark/sql/DataFrameSuite.scala
index 13341645e8ff..30a6e1fe3900 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/DataFrameSuite.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/DataFrameSuite.scala
@@ -2034,6 +2034,28 @@ class DataFrameSuite extends QueryTest with SharedSQLContext {
     }
   }
 
+  test("SPARK-21520: the fields of project contains nondeterministic") {
+    withSQLConf(SQLConf.CASE_SENSITIVE.key -> "false") {
+      withTempPath { path =>
+        val p = path.getAbsolutePath
+        Seq((1, 2, 3), (4, 5, 6)).toDF("a", "b", "c").write.partitionBy("a").parquet(p)
+        val df = spark.read.parquet(p)
+
+        val qe = df.select($"a", rand(10).as('rand))
+        // FileScan parquet [a#38]
+        assert(qe.queryExecution.sparkPlan.inputSet.toString.contains("a#"))
+        assert(!qe.queryExecution.sparkPlan.inputSet.toString.contains("b#"))
+        assert(!qe.queryExecution.sparkPlan.inputSet.toString.contains("c#"))
+
+        val qe2 = df.select($"a", $"b", rand(10).as('rand2))
+        // FileScan parquet [b#70,a#72]
+        assert(qe2.queryExecution.sparkPlan.inputSet.toString.contains("a#"))
+        assert(qe2.queryExecution.sparkPlan.inputSet.toString.contains("b#"))
+        assert(!qe2.queryExecution.sparkPlan.inputSet.toString.contains("c#"))
+      }
+    }
+  }
+
   test("order-by ordinal.") {
     checkAnswer(
       testData2.select(lit(7), 'a, 'b).orderBy(lit(1), lit(2), lit(3)),
diff --git a/sql/hive/src/main/scala/org/apache/spark/sql/hive/HiveStrategies.scala b/sql/hive/src/main/scala/org/apache/spark/sql/hive/HiveStrategies.scala
index caf554d9ea51..d9abf1f3a236 100644
--- a/sql/hive/src/main/scala/org/apache/spark/sql/hive/HiveStrategies.scala
+++ b/sql/hive/src/main/scala/org/apache/spark/sql/hive/HiveStrategies.scala
@@ -26,8 +26,7 @@ import org.apache.spark.sql._
 import org.apache.spark.sql.catalyst.catalog._
 import org.apache.spark.sql.catalyst.expressions._
 import org.apache.spark.sql.catalyst.planning._
-import org.apache.spark.sql.catalyst.plans.logical.{InsertIntoDir, InsertIntoTable, LogicalPlan,
-    ScriptTransformation}
+import org.apache.spark.sql.catalyst.plans.logical._
 import org.apache.spark.sql.catalyst.rules.Rule
 import org.apache.spark.sql.execution._
 import org.apache.spark.sql.execution.command.{CreateTableCommand, DDLUtils}
@@ -239,6 +238,15 @@ private[hive] trait HiveStrategies {
    */
   object HiveTableScans extends Strategy {
     def apply(plan: LogicalPlan): Seq[SparkPlan] = plan match {
+      case p @ Project(fields, child)
+        if !fields.forall(_.deterministic) && p.references.nonEmpty =>
+        collectHiveTableSource(Project(child.output.filter(p.references.contains), child))
+          .map(p => ProjectExec(fields, p)).toList
+
+      case _ => collectHiveTableSource(plan)
+    }
+
+    private def collectHiveTableSource(plan: LogicalPlan): Seq[SparkPlan] = plan match {
       case PhysicalOperation(projectList, predicates, relation: HiveTableRelation) =>
         // Filter out all predicates that only deal with partition keys, these are given to the
         // hive table scan operator to be used for partition pruning.