@Mohammed Fouzan, you don't need to have an Axis bank account, you only have to submit the cheque in your existing account which could be of any bank and in a couple of days the money will get credited in to your account!!
Mohammad its just like anyother cheque you must have received from any other party. So just deposit in your bank account. If dont have one you will have to open one as it is account payee cheque as mentioned.