Disclosed herein is a shift device of a dual clutch transmission capable of simplifying a configuration of a shift control mechanism of the transmission and contributing to saving costs by sharing odd-stage and even-stage select mechanisms and individually including an odd-stage shift mechanism and an even-stage shift mechanism. The shift device of a dual clutch transmission includes: a select guide block (20) moving in a straight direction by a driving of the select motor (10); a pair of control shafts (50) and (60) each shaft moving in a select direction by the straight movement of the select guide block; and a pair of odd-stage and even-stage shift motors (30) and (40) each providing a shaft rotating force to the pair of control shafts (50) and (60) in a shift direction.