A diagnostic apparatus for a vehicle provided with a continuously-variable transmission including a primary pulley, a secondary pulley and a belt looped over the primary and secondary pulleys, such that each of the primary and secondary pulleys includes a hydraulic actuator to which a working fluid is to be supplied. The diagnostic apparatus is configured, in event of occurrence of slippage of the belt on at least one of the primary and secondary pulleys, to infer a factor causing the slippage of the belt, based on at least one of a hydraulic pressure of the working fluid supplied to the hydraulic actuator of the primary pulley and a hydraulic pressure of the working fluid supplied to the hydraulic actuator of the secondary pulley, upon the occurrence of the slippage of the belt.