A shift apparatus for a dual clutch transmission includes a plurality of shift lugs and a shift operating module moving the shift lugs. The apparatus provides a simple structure and sufficient rigidity and durability, in addition to a simple shift of a gear. The apparatus further provides an automatic releasing function that automatically releases the prior shift stage and an active inter-lock function that prevents gears connected to the same clutch from being engaged simultaneously, and enables 6-3-stage and 5-2-stage skip shift.