diff --git a/datafusion/physical-expr/src/window/rank.rs b/datafusion/physical-expr/src/window/rank.rs
index 9bc36728f46ef..86af5b322133c 100644
--- a/datafusion/physical-expr/src/window/rank.rs
+++ b/datafusion/physical-expr/src/window/rank.rs
@@ -141,9 +141,16 @@ impl PartitionEvaluator for RankEvaluator {
         // There is no argument, values are order by column values (where rank is calculated)
         let range_columns = values;
         let last_rank_data = get_row_at_idx(range_columns, row_idx)?;
-        let empty = self.state.last_rank_data.is_empty();
-        if empty || self.state.last_rank_data != last_rank_data {
-            self.state.last_rank_data = last_rank_data;
+        let new_rank_encountered =
+            if let Some(state_last_rank_data) = &self.state.last_rank_data {
+                // if rank data changes, new rank is encountered
+                state_last_rank_data != &last_rank_data
+            } else {
+                // First rank seen
+                true
+            };
+        if new_rank_encountered {
+            self.state.last_rank_data = Some(last_rank_data);
             self.state.last_rank_boundary += self.state.current_group_count;
             self.state.current_group_count = 1;
             self.state.n_rank += 1;
diff --git a/datafusion/physical-expr/src/window/window_expr.rs b/datafusion/physical-expr/src/window/window_expr.rs
index 4211a616e100a..548fae75bd977 100644
--- a/datafusion/physical-expr/src/window/window_expr.rs
+++ b/datafusion/physical-expr/src/window/window_expr.rs
@@ -274,7 +274,7 @@ pub enum WindowFn {
 #[derive(Debug, Clone, Default)]
 pub struct RankState {
     /// The last values for rank as these values change, we increase n_rank
-    pub last_rank_data: Vec<ScalarValue>,
+    pub last_rank_data: Option<Vec<ScalarValue>>,
     /// The index where last_rank_boundary is started
     pub last_rank_boundary: usize,
     /// Keep the number of entries in current rank
diff --git a/datafusion/sqllogictest/test_files/window.slt b/datafusion/sqllogictest/test_files/window.slt
index 864f7dc0a47db..aa083290b4f46 100644
--- a/datafusion/sqllogictest/test_files/window.slt
+++ b/datafusion/sqllogictest/test_files/window.slt
@@ -3801,19 +3801,25 @@ select rank() over (order by 1) rnk from (select 1 a union all select 2 a) x
 1
 1
 
+# support scalar value in ORDER BY
+query I
+select dense_rank() over () rnk from (select 1 a union all select 2 a) x
+----
+1
+1
+
 # support scalar value in both ORDER BY and PARTITION BY, RANK function
-# TODO: fix the test, some issue in RANK
-#query IIIIII
-#select rank() over (partition by 1 order by 1) rnk,
-#       rank() over (partition by a, 1 order by 1) rnk1,
-#       rank() over (partition by a, 1 order by a, 1) rnk2,
-#       rank() over (partition by 1) rnk3,
-#       rank() over (partition by null) rnk4,
-#       rank() over (partition by 1, null, a) rnk5
-#from (select 1 a union all select 2 a) x
-#----
-#1 1 1 1 1 1
-#1 1 1 1 1 1
+query IIIIII
+select rank() over (partition by 1 order by 1) rnk,
+       rank() over (partition by a, 1 order by 1) rnk1,
+       rank() over (partition by a, 1 order by a, 1) rnk2,
+       rank() over (partition by 1) rnk3,
+       rank() over (partition by null) rnk4,
+       rank() over (partition by 1, null, a) rnk5
+from (select 1 a union all select 2 a) x
+----
+1 1 1 1 1 1
+1 1 1 1 1 1
 
 # support scalar value in both ORDER BY and PARTITION BY, ROW_NUMBER function
 query IIIIII