The following year he was named the club captain, led the Eredivisie in scoring with 35 goals in 33 games and was named Dutch Footballer of the Year. He scored 49 goals in all competitions and Ajax won the KNVB Cup. In the 2010–11 season he scored his one hundredth Ajax goal and joined an elite group of players from the club, including Johan Cruyff, Marco van Basten and Dennis Bergkamp, to do so. That season he was also involved in an incident in which he bit the shoulder of PSV player Otman Bakkal during a game. He was branded the "Cannibal of Ajax" and suspended seven games. During his suspension, in January 2011, he transferred to Liverpool for €26.5 million (£22.8 million).
During his partial season at Liverpool, Suárez helped the club move from twelfth in the league in mid-January to finish sixth. In February 2012 Suárez won his first trophy with Liverpool, as they won the League Cup.
In 2011, Suárez scored four goals for Uruguay as they won a record fifteenth Copa América, and he was named Player of the Tournament