An acceleration control method for a dual clutch transmission (DCT) vehicle, may include determining whether an engine speed is lower than a desired shift stage input shaft speed by a controller when a driver's demand for acceleration is verified, determining whether an engine speed increased by the demand for acceleration is equal to or greater than the desired shift stage input shaft speed by the controller, feedback-controlling an engagement-side clutch to reduce a slip caused by a difference between the engine speed and the desired shift stage input shaft speed while maintaining an engine torque by the controller when the engine speed is verified to be equal to or greater than the desired shift stage input shaft speed, and completing control by verifying whether synchronization of the engine speed with the desired shift stage input shaft speed is stabilized.