Born in Cuba, Leinier is the most qualified player born on the island after Capablanca. He is currently the 10th player in the World´s top ranking.
In 2008 in Almaty (Kazakhstan), Leinier became world champion of blitz ahead of Ivanchuk and a long list of famous Grandmasters.
In June 2013, he won the FIDE Grand Prix, held in Thessaloniki, beating twelve other Grand Masters, including Fabiano Caruana, Veselin Topalov and Alexander Grischuk.
In the 2016 Chess Olympiad held in Baku, he won the silver medal defending the first board of his country by scoring 7.5 points in 10 games for an Elo performance rating of 2839. He has accumulated an important list of victories against the world´s strongest players. He played in León in 2010 being beaten in the semifinals by Levon Aronian.