First and foremost, you should have a talk with this player. Mention to him that his constant checking for traps is becoming a major time drag on the campaign, and ask him to do it a bit less often, or only when prompted, so that the game won't be bogged down by constant trap-checking.
If need be, suggest that he only needs to check for traps if you mention that he should check for traps. This assumes a separation of player/character knowledge, but if he's willing to go along with it, you can let him continue to serve as a trap-checker when traps are actually present, without bogging the campaign down with constant trap-checking of empty rooms.
Now if he's still insisting on doing constant trap-checking everywhere he goes, here's a few things you can do to keep things moving along.
Broaden the scope of his checks
You say he checks for traps 'everywhere he goes'. Does this mean every time he enters a room? Every time the party enters a new town? Every time they go to bed? All of these things can get tiring, so try to provide him with a broad trap-checking roll before getting into an area where you will have a lot of action take place. If the party's travelling, have him check for traps once for the entire trip and apply it to however many traps he does (or does not) come across. If they're entering a town, have him roll to check for traps in all the samll buildings they enter once. If they're entering a large building or dungeon, have him check for traps on each floor once.
You will have to run this option by him, and decide if you are okay with it. The result is that he gets one chance to determine how alert he is while looking for traps in an area. If he gets a good roll, he'll find traps in that area very easily. If he doesn't, tough luck. Explain that it will help keep the game moving forward, and allow him to get to the combat sections he does so well in much quicker (preferably mention that bit when the other players aren't around).
Use fewer traps
If he's constantly checking for traps, he may be paranoid of previous traps he's had to encounter. Use fewer, and he'll likely stop checking around quite as often...this assumes you have actually used traps in the past, and that he's not just being paranoid for no reason.
Penalize him for taking too much time
Checking for traps that throughly takes time. If he's checking each room he enters for traps, monsters or enemies that are moving around the area should have a chance to converge on the party while he's doing so. He should definitely not be able to check very throughly in the midst of or immediately prior to battle, lest he use up precious combat actions. Make sure you make it clear that taking up time is the reason this is happening.
Let the party go on without him
There's no reason, if the party members feel that the rogue is being paranoid and taking too much time, that they have to stay with him while he's checking every nook and cranny for traps. If the group decides he's taking up too much time, let them try to go on without him. Make sure they do this in-character though, and don't treat it like they're abandoning the player.