diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 5c74965bffdd7..1437006ee3fb8 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -234,6 +234,7 @@ Other enhancements
   compression library. Compression was also added to the low-level Stata-file writers
   :class:`~pandas.io.stata.StataWriter`, :class:`~pandas.io.stata.StataWriter117`,
   and :class:`~pandas.io.stata.StataWriterUTF8` (:issue:`26599`).
+- :meth:`HDFStore.put` now accepts `track_times` parameter. Parameter is passed to ``create_table`` method of ``PyTables`` (:issue:`32682`).
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/io/pytables.py b/pandas/io/pytables.py
index 345402e619ff2..85fcfd107b121 100644
--- a/pandas/io/pytables.py
+++ b/pandas/io/pytables.py
@@ -984,6 +984,7 @@ def put(
         data_columns: Optional[List[str]] = None,
         encoding=None,
         errors: str = "strict",
+        track_times: bool = True,
     ):
         """
         Store object in HDFStore.
@@ -1010,6 +1011,12 @@ def put(
             Provide an encoding for strings.
         dropna   : bool, default False, do not write an ALL nan row to
             The store settable by the option 'io.hdf.dropna_table'.
+        track_times : bool, default True
+            Parameter is propagated to 'create_table' method of 'PyTables'.
+            If set to False it enables to have the same h5 files (same hashes)
+            independent on creation time.
+
+            .. versionadded:: 1.1.0
         """
         if format is None:
             format = get_option("io.hdf.default_format") or "fixed"
@@ -1027,6 +1034,7 @@ def put(
             data_columns=data_columns,
             encoding=encoding,
             errors=errors,
+            track_times=track_times,
         )
 
     def remove(self, key: str, where=None, start=None, stop=None):
@@ -1626,6 +1634,7 @@ def _write_to_group(
         data_columns=None,
         encoding=None,
         errors: str = "strict",
+        track_times: bool = True,
     ):
         group = self.get_node(key)
 
@@ -1688,6 +1697,7 @@ def _write_to_group(
             dropna=dropna,
             nan_rep=nan_rep,
             data_columns=data_columns,
+            track_times=track_times,
         )
 
         if isinstance(s, Table) and index:
@@ -4106,8 +4116,8 @@ def write(
         dropna=False,
         nan_rep=None,
         data_columns=None,
+        track_times=True,
     ):
-
         if not append and self.is_exists:
             self._handle.remove_node(self.group, "table")
 
@@ -4137,6 +4147,8 @@ def write(
             # set the table attributes
             table.set_attrs()
 
+            options["track_times"] = track_times
+
             # create the table
             table._handle.create_table(table.group, **options)
 
diff --git a/pandas/tests/io/pytables/test_store.py b/pandas/tests/io/pytables/test_store.py
index c937f9ac42818..fe59b989bab7e 100644
--- a/pandas/tests/io/pytables/test_store.py
+++ b/pandas/tests/io/pytables/test_store.py
@@ -1,10 +1,12 @@
 import datetime
 from datetime import timedelta
 from distutils.version import LooseVersion
+import hashlib
 from io import BytesIO
 import os
 from pathlib import Path
 import re
+import time
 from warnings import catch_warnings, simplefilter
 
 import numpy as np
@@ -296,6 +298,49 @@ def test_keys(self, setup_path):
             assert set(store.keys()) == expected
             assert set(store) == expected
 
+    def test_no_track_times(self, setup_path):
+
+        # GH 32682
+        # enables to set track_times (see `pytables` `create_table` documentation)
+
+        def checksum(filename, hash_factory=hashlib.md5, chunk_num_blocks=128):
+            h = hash_factory()
+            with open(filename, "rb") as f:
+                for chunk in iter(lambda: f.read(chunk_num_blocks * h.block_size), b""):
+                    h.update(chunk)
+            return h.digest()
+
+        def create_h5_and_return_checksum(track_times):
+            with ensure_clean_path(setup_path) as path:
+                df = pd.DataFrame({"a": [1]})
+
+                with pd.HDFStore(path, mode="w") as hdf:
+                    hdf.put(
+                        "table",
+                        df,
+                        format="table",
+                        data_columns=True,
+                        index=None,
+                        track_times=track_times,
+                    )
+
+                return checksum(path)
+
+        checksum_0_tt_false = create_h5_and_return_checksum(track_times=False)
+        checksum_0_tt_true = create_h5_and_return_checksum(track_times=True)
+
+        # sleep is necessary to create h5 with different creation time
+        time.sleep(1)
+
+        checksum_1_tt_false = create_h5_and_return_checksum(track_times=False)
+        checksum_1_tt_true = create_h5_and_return_checksum(track_times=True)
+
+        # checksums are the same if track_time = False
+        assert checksum_0_tt_false == checksum_1_tt_false
+
+        # checksums are NOT same if track_time = True
+        assert checksum_0_tt_true != checksum_1_tt_true
+
     def test_keys_ignore_hdf_softlink(self, setup_path):
 
         # GH 20523