Kohli struck a classy 204 as India made their third consecutive score of over 600 before declaring on 687-6.
The India captain made 235 against England in December, as well as 211 against New Zealand in October and 200 against West Indies in July.
India, the world's top Test team, have not lost a home Test series since 2012.
Murali Vijay scored 108 and Wriddhiman Saha an unbeaten 106 as India made their highest Test score against Bangladesh.
Kohli, who captains India in all three formats, hit 24 boundaries on his way to a double century, taking his Test average to 50.10.
Virat Kohli became the first Test batsman to register double centuries in four successive series as India dominated Bangladesh in Hyderabad.