The 27-year-old scored 31 goals and made 12 assists in 33 Premier League appearances to help the Reds to a second-place finish.
Suarez also collected the Barclays Golden Boot award for finishing the campaign as the top goal-scorer in the Premier League.
Meanwhile, Tony Pulis has been crowned the Barclays manager of the season.
The Crystal Palace boss guided the Eagles to an 11th place finish in the Barclays Premier League after joining the club in November when they had only four points and were bottom of the table. Pulis was presented with his award at Monday night’s LMA awards dinner.
The Barclays Golden Glove award for 2013-14 has been jointly won by Chelsea’s Petr Cech and Arsenal’s Wojciech Szczesny.
The two goalkeepers kept 16 clean sheets each this season – Cech doing so in 34 Barclays Premier League appearances and Szczesny in 37. This is the third time that Cech has won the award, and the first time for Szczesny.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news