A diagnostic method of determining clutch failure of a dual clutch transmission (DCT) includes comparing, by a controller, a wheel torque of a vehicle with a driving load torque of the vehicle, confirming, by the controller, whether or not the vehicle is driving, if, as a result of comparing step, the wheel torque is greater than the driving load torque, releasing, by the controller, a gear engaged with a non-drive shaft, if, as a result of the confirming step, the vehicle is in a stopped state, reconfirming, by the controller, whether or not the vehicle is driving, after the releasing step, and judging, by the controller, that a transmission clutch of the non-drive shaft fails, if, as a result of the reconfirming step, the vehicle is driving.