diff --git a/datafusion/core/tests/physical_optimizer/mod.rs b/datafusion/core/tests/physical_optimizer/mod.rs
index 98e7b87ad215..777c26e80e90 100644
--- a/datafusion/core/tests/physical_optimizer/mod.rs
+++ b/datafusion/core/tests/physical_optimizer/mod.rs
@@ -30,3 +30,4 @@ mod projection_pushdown;
 mod replace_with_order_preserving_variants;
 mod sanity_checker;
 mod test_utils;
+mod window_optimize;
diff --git a/datafusion/core/tests/physical_optimizer/window_optimize.rs b/datafusion/core/tests/physical_optimizer/window_optimize.rs
new file mode 100644
index 000000000000..ba0ffb022a03
--- /dev/null
+++ b/datafusion/core/tests/physical_optimizer/window_optimize.rs
@@ -0,0 +1,90 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+#[cfg(test)]
+mod test {
+    use arrow::array::{Int32Array, RecordBatch};
+    use arrow_schema::{DataType, Field, Schema};
+    use datafusion_common::Result;
+    use datafusion_datasource::memory::MemorySourceConfig;
+    use datafusion_datasource::source::DataSourceExec;
+    use datafusion_execution::TaskContext;
+    use datafusion_expr::WindowFrame;
+    use datafusion_functions_aggregate::count::count_udaf;
+    use datafusion_physical_expr::aggregate::AggregateExprBuilder;
+    use datafusion_physical_expr::expressions::{col, Column};
+    use datafusion_physical_expr::window::PlainAggregateWindowExpr;
+    use datafusion_physical_plan::windows::BoundedWindowAggExec;
+    use datafusion_physical_plan::{common, ExecutionPlan, InputOrderMode};
+    use std::sync::Arc;
+
+    /// Test case for <https://github.com/apache/datafusion/issues/16308>
+    #[tokio::test]
+    async fn test_window_constant_aggregate() -> Result<()> {
+        let source = mock_data()?;
+        let schema = source.schema();
+        let c = Arc::new(Column::new("b", 1));
+        let cnt = AggregateExprBuilder::new(count_udaf(), vec![c])
+            .schema(schema.clone())
+            .alias("t")
+            .build()?;
+        let parition = [col("a", &schema)?];
+        let frame = WindowFrame::new(None);
+        let plain =
+            PlainAggregateWindowExpr::new(Arc::new(cnt), &parition, &[], Arc::new(frame));
+
+        let bounded_agg_exec = BoundedWindowAggExec::try_new(
+            vec![Arc::new(plain)],
+            source,
+            InputOrderMode::Linear,
+            true,
+        )?;
+        let task_ctx = Arc::new(TaskContext::default());
+        common::collect(bounded_agg_exec.execute(0, task_ctx)?).await?;
+
+        Ok(())
+    }
+
+    pub fn mock_data() -> Result<Arc<DataSourceExec>> {
+        let schema = Arc::new(Schema::new(vec![
+            Field::new("a", DataType::Int32, true),
+            Field::new("b", DataType::Int32, true),
+        ]));
+
+        let batch = RecordBatch::try_new(
+            Arc::clone(&schema),
+            vec![
+                Arc::new(Int32Array::from(vec![
+                    Some(1),
+                    Some(1),
+                    Some(3),
+                    Some(2),
+                    Some(1),
+                ])),
+                Arc::new(Int32Array::from(vec![
+                    Some(1),
+                    Some(6),
+                    Some(2),
+                    Some(8),
+                    Some(9),
+                ])),
+            ],
+        )?;
+
+        MemorySourceConfig::try_new_exec(&[vec![batch]], Arc::clone(&schema), None)
+    }
+}
diff --git a/datafusion/physical-expr/src/window/window_expr.rs b/datafusion/physical-expr/src/window/window_expr.rs
index 59f9e1780731..d994e8be1d24 100644
--- a/datafusion/physical-expr/src/window/window_expr.rs
+++ b/datafusion/physical-expr/src/window/window_expr.rs
@@ -277,6 +277,11 @@ pub trait AggregateWindowExpr: WindowExpr {
         let values = self.evaluate_args(record_batch)?;
 
         if self.is_constant_in_partition() {
+            if not_end {
+                let field = self.field()?;
+                let out_type = field.data_type();
+                return Ok(new_empty_array(out_type));
+            }
             accumulator.update_batch(&values)?;
             let value = accumulator.evaluate()?;
             return value.to_array_of_size(record_batch.num_rows());