The present disclosure relates to a shift control apparatus of a vehicle and its method. In particular, the shift control apparatus includes: a transmission including a first clutch and a second clutch; a torque source to generate power for driving a vehicle; a data detector to detect a vehicle state data; and a vehicle controller to connect a current stage synchronizer to a next stage driving gear if the vehicle state data satisfy a shift condition, release the first clutch to be connected to the driving gear of a current stage, perform a speed control of a torque source while maintaining the second clutch connected to the driving gear of the next stage in a slip state, and release the second clutch and connect the first clutch if the vehicle stage data satisfy a speed control completion condition to complete a shift to a target stage.