A shift control method can be used for a vehicle with a dual-clutch transmission (DCT). A controller determines whether or not a power-on upshift is initiated in a state in which a high performance mode has been selected. The controller performs a torque phase in which a coupling-side clutch torque is gradually increased and a release-side clutch torque is gradually released. The coupling-side clutch torque is gradually increased to a target coupling-side clutch torque corresponding to a value obtained by adding a push feel torque to a base torque. The controller performs an inertia phase in which the coupling-side clutch torque is gradually increased while tracing an engine torque such that an engine speed is synchronized with a coupling-side clutch speed. The controller completes speed change through gradual decrease of the coupling-side clutch torque.