Grant had a league-high 50 goals and added 66 assists for 116 points, one more than John Tavares' old record set with Buffalo in 2001.
The 37-year-old Grant, who was selected first overall in the 1999 NLL entry draft, helped the 11-5 Mammoth to a second-place finish in the Western Division this season.
"This is a tremendous honour, especially after being written off as an elite player by some in the past few years," Grant said in a release. "This is a team award more than an individual award, and it wouldn't have happened if (GM Steve Govett) hadn't put great pieces around me."
Garrett Billings of the Toronto Rock was second and Dan Dawson of the Philadelphia Wings was third in voting by the league's board of governors, general managers and head coaches.
It was the second MVP award of Grant's career. He also took the honour while playing for the Rochester Knighthawks in 2007.
Grant, from Peterborough, Ont., reached several plateaus this season.
The Mammoth assistant captain became the fifth player in league history to record 1,000 career points. He also joined Tavares and Hall of Famer Gary Gait as the only players to reach the 500-goal plateau.
"It's a real pleasure to be around him," Mammoth coach Bob Hamley said after Grant reached the goals plateau March 3 against Buffalo. "He's a great lacrosse player and an even better person."
Billings set a new NLL record for assists in a season by registering 82 for the East Division-champion Rock. His 114 points eclipsed current Toronto captain Colin Doyle's club record of 111.
Dawson, who broke his own league record for assists in a season before being overtaken by Billings, finished with 103 points (25-78). He broke Athan Iannucci's club record of 100 points set four years earlier.
The NLL rookie of the year award will be announced Friday.