diff --git a/llama_cpp/llama.py b/llama_cpp/llama.py
index 8b7dee0..688b2a7 100644
--- a/llama_cpp/llama.py
+++ b/llama_cpp/llama.py
@@ -443,7 +443,8 @@ class Llama:
             # Save logits
             rows = n_tokens if self.params.logits_all else 1
             cols = self._n_vocab
-            self.scores[self.n_tokens : self.n_tokens + n_tokens, :].reshape(-1)[:] = llama_cpp.llama_get_logits(self.ctx)[:rows * cols]
+            offset = 0 if self.params.logits_all else n_tokens - 1 # NOTE: Only save the last token logits if logits_all is False
+            self.scores[self.n_tokens + offset: self.n_tokens + n_tokens, :].reshape(-1)[:] = llama_cpp.llama_get_logits(self.ctx)[:rows * cols]
             # Update n_tokens
             self.n_tokens += n_tokens