The Uruguay international scored 31 goals and produced 12 assists as his team finished two points behind champions Manchester City in a thrilling title race in the top flight.
Suarez, 27, collected the Barclays Golden Boot award for finishing the campaign as the top goal scorer in the Premier League.
Chelsea's Petr Cech and Arsenal's Wojciech Szczesny could not be separated as they were joint winners of the Barclays Golden Glove award for 2013/14.
The two keepers kept 16 clean sheets each this season - Cech doing so in 34 league games and Szczesny in 37. This is the third time Cech has won the award, and the first time for Szczesny.
Tony Pulis stole the honours in the managerial stakes with the Crystal Palace boss scooping the Barclays Manager of the Season award.
The Welshman guided the Eagles to 11th place after joining the club in November when they had only four points and were bottom of the table. He was presented with his award at Monday night's LMA awards dinner.
Voting was made by the Barclays Awards Panel, which includes representatives from football's governing bodies, the media and fans.