His first-class career began in October 2011, when he turned out for Rangpur Division against Dhaka Division. A modest opening season gave way to a stronger second one, which brought him a century and a fifty. The 2014 Under-19 World Cup in Abu Dhabi gave him a real lift: he collected 239 runs across only four innings.
That tournament fed into a productive domestic run. In the Dhaka Premier League he finished second on the run list, and he then went one better in the National Cricket League for Rangpur Division, topping the scoring with five hundreds, over 1000 runs and an average of 85.33.
India were the opponents for his Test debut in June 2015, when he made a fluent 44 from 45 deliveries. A first Test half-century followed against South Africa, then the top-ranked side, yet he was out of the national team for the next two years. He returned to enjoy a standout 2018, which included 94 in a drawn Test against Sri Lanka at Chattogram, a first T20I fifty against West Indies at Lauderhill and a first ODI century, against India at the Asia Cup. India would feel his bat again in major events, with fifties at the 2022 T20 World Cup and the 2023 ODI World Cup.
His first Test hundred arrived in 2021, six years on from his debut: 114 against Pakistan at Chattogram. Two more soon followed, 102 against New Zealand at Christchurch and 141 against Sri Lanka at Mirpur. In 2025, after Najmul Hossain Shanto gave up the role, Litton was appointed captain of the T20I team.