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 was proclaimed world blitz chess champion 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 Grandmasters, 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 strongest players of the world. He played in León in 2010, losing in the semifinals to Levon Aronian.
Leinier was proclaimed the winner of the XXXIII Magistral de León in 2020, defeating in the final the GM from León Jaime Santos.