First of all get the engine mountings checked... If they are ok then get your car properly tuned...
Note 1 thing that till the time your car's engine is not properly warm, you will feel the vibration inside your car. But after some time when the engine is properly warm, this vibration will be removed. In winters you can also use choke for first five minutes till the engine is warm to avoid vibration as too much vibration is not good for the engine as well....