A power transmission device for a vehicle comprises a first power transmitting path for transmitting engine output to a wheel side via a reduction gear, a second power transmitting path for transmitting engine output to the wheel side via a stepless speed change gear mechanism, a path switching clutch for switching between the paths to transmit by one of the paths, a switch-over control part for controlling switch-over operation of the clutch according to a driving condition of the vehicle, and a rotational condition abrupt change restraining part for restraining an abrupt change of a rotational condition of an engine output shaft at switch-over between the paths. The restraining part adjusts to conform rotating speeds of the input and output sides of the clutch to each other at switch-over of the clutch, or conform output torque to the wheel side between before and after switch-over of the clutch. Thus, an abrupt change of rotation of the engine output shaft is restrained to prevent a shock owing to switch-over, and the durability of a friction element is enhanced.