diff --git a/d3rlpy/logging/file_adapter.py b/d3rlpy/logging/file_adapter.py
index e6d58a80..637402c1 100644
--- a/d3rlpy/logging/file_adapter.py
+++ b/d3rlpy/logging/file_adapter.py
@@ -42,10 +42,12 @@ class FileAdapter(LoggerAdapter):
 
     _algo: AlgProtocol
     _logdir: str
+    _is_model_watched: bool
 
     def __init__(self, algo: AlgProtocol, logdir: str):
         self._algo = algo
         self._logdir = logdir
+        self._is_model_watched = False
         if not os.path.exists(self._logdir):
             os.makedirs(self._logdir)
             LOG.info(f"Directory is created at {self._logdir}")
@@ -91,14 +93,29 @@ def watch_model(
         step: int,
     ) -> None:
         assert self._algo.impl
+
+        # write header at the first call
+        if not self._is_model_watched:
+            self._is_model_watched = True
+            for name, grad in self._algo.impl.modules.get_gradients():
+                path = os.path.join(self._logdir, f"{name}_grad.csv")
+                with open(path, "w") as f:
+                    print(
+                        ",".join(
+                            ["epoch", "step", "min", "max", "mean", "std"]
+                        ),
+                        file=f,
+                    )
+
         for name, grad in self._algo.impl.modules.get_gradients():
             path = os.path.join(self._logdir, f"{name}_grad.csv")
             with open(path, "a") as f:
                 min_grad = grad.min()
                 max_grad = grad.max()
-                mean_grad = grad.mean()
+                mean = grad.mean()
+                std = grad.std()
                 print(
-                    f"{epoch},{step},{min_grad},{max_grad},{mean_grad}",
+                    f"{epoch},{step},{min_grad},{max_grad},{mean},{std}",
                     file=f,
                 )