Jim Brown's Son BEASTING OUT ... As Lacrosse Prodigy!

Jim Brown's teenage son is following in his father's footsteps ... as a killer lacrosse player -- and TMZ Sports has the video!

FYI, Jim has been hailed as one of the GREATEST lacrosse players of all time (in addition to that whole NFL Hall of Fame thing) ... and it's clear his son, Aris, has his father's gifts.

Aris is a freshman at Sierra Canyon High School in L.A. where he's already crushed a few impressive goals ... showing off speed, strength and shot power.

We spoke with Jim Brown who tells us, "It's great that he's playing lacrosse and that he loves it!"