Skipper Cook was 95no overnight after the first day of the two-day game, the opening match of England???s tour of the West Indies.
He completed his century within 10 minutes of the second day. A controlled thick edge from the first ball of the day brought him an 11th??boundary of the innings and in the following over he punched the ball for two??off the back foot, bringing up his century off the 200th ball.
He offered a gentle wave of the bat, shook hands with his batting partner Gary Ballance and walked back off to the pavilion with his score on 101no.
His retirement brought Ian Bell to the crease, with all of England???s batsmen hoping for some time in the middle, albeit against a friendly bowling attack.
England???s bowlers enjoyed an impressive start to the tour on Monday, bowling the hosts out for just 59.
Cook’s last century for England was his 130 against New Zealand in a Headingley Test match in May 2013.