A power transmission apparatus for an engine of a vehicle. The apparatus includes a starting clutch for smoothly connecting rotation of a crankshaft to a transmission upon starting of the vehicle, a hydrostatic continuously variable transmission for performing speed change depending upon a capacity difference between a swash plate hydraulic pump and a swash plate hydraulic motor to transmit rotation of the crankshaft at a reduced speed to a driving wheel, and a slider for moving a ball screw back and forth to change the angle of the swash plate of the swash plate hydraulic motor. The starting clutch can be a torque converter.