Try pouring some bleach down there, let it sit for awhile. If yo ucan get the grill off, you could try using a brush to clean the pipe above the trap.
One (unfortuneately) common reason for a smelly shower is an incorrectly built pan. That doesn't mean one that leaks (course that could be a problem too). For some reason, many plumbers seem to think that tile and grout is waterproof, and the liner can sit flat on the floor. It can't, and tile and grout aren't. The liner should be installed on a presloped bed. Gradually, a little water will get under the top of the tile, begin to saturate the stuff underneath, and stay wet unless the shower is allowed to dry out inbetween (not likely in a daily use). Eventually, that stagnet water will smell like a swamp. If you have a solid manufactured pan, this doesn't happen, although crud can build up in the textured surface.
What kind of shower is it?