A method for switching a call by a User Equipment (UE) supporting a Voice Call Continuity (VCC) scheme in a mobile communication system is provided. The method includes detecting that there is a need for switching a voice call from a first access network to a second access network that is different from the first access network while the UE supporting the VCC scheme transmits/receives data in the first access network through an old bearer which is set up with the other party UE, performing a new bearer set up operation with the second access network, and transmitting/receiving voice data with the other party UE through the old bearer in the first access network and transmitting/receiving voice data with the other party UE through the new bearer in the second access network until a point in time.