diff --git a/planner/core/rule_inject_extra_projection.go b/planner/core/rule_inject_extra_projection.go
index 9b629b894040f..a2bcbcf28e3eb 100644
--- a/planner/core/rule_inject_extra_projection.go
+++ b/planner/core/rule_inject_extra_projection.go
@@ -99,9 +99,10 @@ func injectProjBelowAgg(aggPlan PhysicalPlan, aggFuncs []*aggregation.AggFuncDes
 			}
 			projExprs = append(projExprs, arg)
 			newArg := &expression.Column{
-				RetType: arg.GetType(),
-				ColName: model.NewCIStr(fmt.Sprintf("col_%d", len(projSchemaCols))),
-				Index:   cursor,
+				UniqueID: aggPlan.context().GetSessionVars().AllocPlanColumnID(),
+				RetType:  arg.GetType(),
+				ColName:  model.NewCIStr(fmt.Sprintf("col_%d", len(projSchemaCols))),
+				Index:    cursor,
 			}
 			projSchemaCols = append(projSchemaCols, newArg)
 			f.Args[i] = newArg
diff --git a/planner/core/task.go b/planner/core/task.go
index f19621dc2552a..e22e3faaab0e9 100644
--- a/planner/core/task.go
+++ b/planner/core/task.go
@@ -508,18 +508,27 @@ func (p *basePhysicalAgg) newPartialAggregate() (partial, final PhysicalPlan) {
 func (p *PhysicalStreamAgg) attach2Task(tasks ...task) task {
 	t := tasks[0].copy()
 	if cop, ok := t.(*copTask); ok {
-		partialAgg, finalAgg := p.newPartialAggregate()
-		if partialAgg != nil {
-			if cop.tablePlan != nil {
-				partialAgg.SetChildren(cop.tablePlan)
-				cop.tablePlan = partialAgg
-			} else {
-				partialAgg.SetChildren(cop.indexPlan)
-				cop.indexPlan = partialAgg
+		// We should not push agg down across double read, since the data of second read is ordered by handle instead of index.
+		// The `doubleReadNeedProj` is always set if the double read needs to keep order. So we just use it to decided
+		// whether the following plan is double read with order reserved.
+		if !cop.doubleReadNeedProj {
+			partialAgg, finalAgg := p.newPartialAggregate()
+			if partialAgg != nil {
+				if cop.tablePlan != nil {
+					cop.finishIndexPlan()
+					partialAgg.SetChildren(cop.tablePlan)
+					cop.tablePlan = partialAgg
+				} else {
+					partialAgg.SetChildren(cop.indexPlan)
+					cop.indexPlan = partialAgg
+				}
 			}
+			t = finishCopTask(p.ctx, cop)
+			attachPlan2Task(finalAgg, t)
+		} else {
+			t = finishCopTask(p.ctx, cop)
+			attachPlan2Task(p, t)
 		}
-		t = finishCopTask(p.ctx, cop)
-		attachPlan2Task(finalAgg, t)
 	} else {
 		attachPlan2Task(p, t)
 	}