Opting to bat, England Lions reached 290 for two in 84 overs at the County Ground.
The former England captain, who is part of a strong Lions XI featuring six Test players, reached his hundred from 173 balls. Cook was unbeaten on 145 off 229 balls, having found the fence 21 times.
Leading the side, opener Rory Burns (5) was dismissed early, allowing fellow England hopeful Nick Gubbins to join Cook at the crease in the fourth over.
The duo of Cook and Gubbins put on 155 runs for the second wicket before the younger player fell to Ankit Rajpoot for 73 in the afternoon session. Gubbins hit seven fours and a six while facing 155 balls.
Cook was then involved in a century partnership with another current Test player, Dawid Malan, who was batting on 48 off 112 balls. The left-handed Cook eased his way through the nineties and went to three figures with a boundary off Navdeep Saini in the 68th over.
For India A, Rajpoot and Saini picked up a wicket each on a day when rewards were hard to come by.
First Published: July 16, 2018, 10:53 PM IST