diff --git a/deepmd/entrypoints/compress.py b/deepmd/entrypoints/compress.py
index 1222b1e51b..3c80965bce 100644
--- a/deepmd/entrypoints/compress.py
+++ b/deepmd/entrypoints/compress.py
@@ -7,6 +7,7 @@
 from deepmd.common import j_loader
 from deepmd.utils.argcheck import normalize
 from deepmd.utils.compat import convert_input_v0_v1
+from deepmd.utils.errors import GraphTooLargeError
 
 from .freeze import freeze
 from .train import train
@@ -79,7 +80,6 @@ def compress(
     jdata["training"]["numb_steps"] = jdata["training"]["save_freq"]
     jdata = normalize(jdata)
 
-
     # check the descriptor info of the input file
     assert (
         jdata["model"]["descriptor"]["type"] == "se_a" or jdata["model"]["descriptor"]["type"] == "se_e2_a"
@@ -94,15 +94,23 @@ def compress(
     control_file = "compress.json"
     with open(control_file, "w") as fp:
         json.dump(jdata, fp, indent=4)
-    train(
-        INPUT=control_file,
-        init_model=None,
-        restart=None,
-        output=control_file,
-        mpi_log=mpi_log,
-        log_level=log_level,
-        log_path=log_path,
-    )
+    try:
+        train(
+            INPUT=control_file,
+            init_model=None,
+            restart=None,
+            output=control_file,
+            mpi_log=mpi_log,
+            log_level=log_level,
+            log_path=log_path,
+        )
+    except GraphTooLargeError as e:
+        raise RuntimeError(
+            "The uniform step size of the tabulation's first table is %f, " 
+            "which is too small. This leads to a very large graph size, "
+            "exceeding protobuf's limitation (2 GB). You should try to "
+            "increase the step size." % step
+        ) from e
 
     # stage 2: freeze the model
     log.info("\n\n")
diff --git a/deepmd/train/trainer.py b/deepmd/train/trainer.py
index 7fa29635cf..8f283b61cf 100644
--- a/deepmd/train/trainer.py
+++ b/deepmd/train/trainer.py
@@ -3,6 +3,7 @@
 import os
 import time
 import shutil
+import google.protobuf.message
 import numpy as np
 from deepmd.env import tf
 from deepmd.env import default_tf_session_config
@@ -19,6 +20,7 @@
 from deepmd.descriptor import DescrptHybrid
 from deepmd.model import EnerModel, WFCModel, DipoleModel, PolarModel, GlobalPolarModel
 from deepmd.loss import EnerStdLoss, EnerDipoleLoss, TensorLoss
+from deepmd.utils.errors import GraphTooLargeError
 from deepmd.utils.learning_rate import LearningRateExp
 from deepmd.utils.neighbor_stat import NeighborStat
 from deepmd.utils.sess import run_sess
@@ -542,7 +544,14 @@ def train (self, train_data, valid_data=None) :
                     train_time = 0
                 if self.save_freq > 0 and cur_batch % self.save_freq == 0 and self.run_opt.is_chief :
                     if self.saver is not None :
-                        self.saver.save (self.sess, os.getcwd() + "/" + self.save_ckpt)
+                        try:
+                            self.saver.save (self.sess, os.getcwd() + "/" + self.save_ckpt)
+                        except google.protobuf.message.DecodeError as e:
+                            raise GraphTooLargeError(
+                                "The graph size exceeds 2 GB, the hard limitation of protobuf."
+                                " Then a DecodeError was raised by protobuf. You should "
+                                "reduce the size of your model."
+                            ) from e
                         log.info("saved checkpoint %s" % self.save_ckpt)
         if self.run_opt.is_chief: 
             fp.close ()
diff --git a/deepmd/utils/errors.py b/deepmd/utils/errors.py
new file mode 100644
index 0000000000..d7b62383f1
--- /dev/null
+++ b/deepmd/utils/errors.py
@@ -0,0 +1,2 @@
+class GraphTooLargeError(Exception):
+    pass