this is my first time in London ,what is the best way to get to Covent Garden from Gatwick airport. (group of 4 ) . should I buy a train pass.
Probably the best route would be...
http://www.gatwickexpress.com/
Gatwick Express to Victoria, then a Black Cab to your hotel.
Approx. cost for GE is £30pp return, and a Black Cab would be under £20 total.
The Gatwick Express is premium fare - First Capital Connect trains to Blackfriars are almost as fast, and are cheaper.
There's no station that trains from Gatwick arrive at that would be easy to get to Covent Garden, so I would agree with a taxi. If you are going before the end of this year, be warned that Covent Garden tube station is undergoing renovation works, exit only at all times and only eastbound trains calling at weekends. Use Holborn or Leicester Square stations instead.
I don't understand what you mean by "train pass". Do you mean a London transport pass, or a national train pass. If you are only travelling from Gatwick to London and possibly back, there's no need to get a national pass.