Black smoke is a good sign ,nothing to worry about.
Our friend quicksilver pointed out that useful thread and if you read post #2 you will find a good tip..Air filter!

Black smoke on standstill can be the engine not getting enough air or is over fuelling !Remember that at standstill ,the engine is not under load.Shortage of air can be a clogged air filter or a leak in a turbo,inlet pipe or a vacuum.
As soon as you drive off ,the engine sucks more air and black smoke not so noticeable!
Overfuelling ,can be a leaking injector but its all related to air supply as not enough air ,it will emit black smoke anyway.
The other thing that comes to mind and probably maybe it ,is your car having a remap and the mapper increased the fuel volume too much at idle,hence it smoking and then clearing up as you drive away and you have load and boost pressure.
Difficult to tell since you havent given us much info on your car.