The Grecians enjoyed most of the possession but failed to break the deadlock despite creating a host of chances. Grimsby were also a threat and were good value for a point in an entertaining encounter.
Both sides stroked the ball around well in the first half without looking particularly dangerous.
Exeter came close to opening the scoring with the first attack of the game in the tenth minute. Marcus Stewart's fine cross from the right was met by Steve Tully and his powerful header was well saved by Phil Barnes at full stretch.
Town responded when Nick Hegarty picked out Nathan Jarman and the striker dragged the ball wide of the post.
Hegarty winger forced Paul Jones to block his low shot from 15 yards. The winger then picked out Peter Bore with a fine cross and the striker headed past the post.
On the stroke of half-time Grimsby's Tom Newey should have been shown red for thrusting his head in the face of Matt Taylor, but the defender escaped with a caution.
After the break Liam Trotter pounced on a loose ball and forced Jones to save well with a shot from the edge of the box.
Taylor headed narrowly wide from Matthew Gill's corner and it looked only a matter of time before Exeter found an opener.
Grimsby remained a threat and Hegarty volleyed narrowly wide from the edge of the box following a half cleared corner.
In the dying seconds Taylor could have grabbed the win for City when he headed Gill's cross onto the roof of the net and the Grecians had to be content with a point.