An apparatus and method of using the apparatus for learning a clutch torque of a Dual Clutch Transmission (DCT) includes judging whether shifting begins, controlling torque transmission of a coupling-side clutch and a release-side clutch to cross each other while following a coupling-side target clutch torque when shifting begins, and calculating and storing a learning value, after the controlling has begun, using a function determined by the relationship between an average value of an engine angular acceleration and a coupling-side shifter input-shaft angular acceleration, engine rotation inertia, and a torque compensated to the torque transmission of the coupling-side clutch for reducing a slippage of the release-side clutch by feedback control during a torque handover interval.