1. A method for transmitting data in a data communication system having a transmitting data terminal and a mobile terminal, the method comprising the steps of: establishing a voice communication channel between said mobile terminal and a receiving data terminal using said data communication system set to a Voice mode; setting said data communication system to a Data mode without disconnecting said voice communication channel by transmitting a first connection request and a receiving side telephone number to said mobile terminal; establishing a data communication channel between said transmitting and receiving data terminals; and transmitting data by said transmitting data terminal to said receiving data terminal through said data communication channel.