Here's proof Bill Belichick is secretly a happy, smilin', ooey-gooey romantic ... courtesy of a lovey-dovey photo shoot with his girlfriend!!

The New England Patriots coach showed off his MUCH softer side with his longtime GF, Linda Holliday, for N Magazine ... strolling through meadows, holding hands, and other mushy stuff.

B.B.'s only wearing one of his Super Bowl rings, though (he went with S.B. 49) ... and even lets Holliday wear it on THAT finger for a couple pics.

The shoot almost comes off as a wedding photo shoot.

Soooooo ... Bill gettin' another ring this year???

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N Magazine