diff --git a/vllm/attention/backends/utils.py b/vllm/attention/backends/utils.py
index 2b8c373178ab3..e451cd5522d18 100644
--- a/vllm/attention/backends/utils.py
+++ b/vllm/attention/backends/utils.py
@@ -218,9 +218,18 @@ def build(self, seq_lens: List[int], query_lens: List[int],
             # The shape of graph_block_tables is
             # [max batch size, max context len // block size].
             input_block_tables = self.runner.graph_block_tables[:batch_size]
+            max_blocks = input_block_tables.shape[1]
             for i, block_table in enumerate(self.block_tables):
                 if block_table:
-                    input_block_tables[i, :len(block_table)] = block_table
+                    num_blocks = len(block_table)
+                    if num_blocks <= max_blocks:
+                        input_block_tables[i, :num_blocks] = block_table
+                    else:
+                        # It may be possible to have more blocks allocated due
+                        # to lookahead slots of multi-step, however, they are
+                        # not used anyway, so can be safely ignored.
+                        input_block_tables[
+                            i, :max_blocks] = block_table[:max_blocks]
             block_tables = torch.from_numpy(input_block_tables).to(
                 device, non_blocking=True)
         else: