A shift control method for a vehicle with a double clutch transmission (DCT) is configured such that when a power-on upshift is initiated, during a target time for a controller to perform a torque phase, a release-side clutch is gradually released, an engine torque is gradually increased to a basic engine torque or more, and an engagement-side clutch torque is increased according to an increase in the engine torque and a vehicle speed; and when the release-side clutch is completely released, the controller reduces the engine torque while gradually reducing the engagement-side clutch torque to be equal to the basic engine torque, to perform an inertia phase such that an engine speed is synchronized with an engagement-side clutch speed.