2008 Mazda Mazda6 -Vibrates

Why my car vibrates after ignition.

Good example of why I would like to see a 140 character minimum on initial posts.

So let me guess. You are saying the engine vibrates more than usual at idle when first started?
First supply the USUAL necessary information:
Miles
Transmission
Engine size
CEL status

Add to this: how long you’ve had the problem, whether it’s happened before, whether it’s associated with something else that happened recently (service, accidents, your 16yr old cousin drove it to the beach, …), whether it changes with either engine or road speed (and which), is there an associated noise, where the vibration appears to be located…

A certain amount of vibration is normal for a 4 cylinder engine if you have one. If there’s pronounced vibration it could be from a number of causes. The engine could be idling rough; that could be a bad spark plug, poor compression, fuel system problems, etc. The engine mounts could be bad. Way too many possibilities and not enough information. Is the check engine light on perchance?