A power transmission apparatus for a vehicle which is used for a four-wheel drive vehicle driving both the front and rear wheels by a driving force from an engine, in which a discharge amount of a hydraulic pump provided between a front wheel drive shaft and a rear wheel drive shaft to generate hydraulic pressure by a rotation speed difference between the two rotary shafts is desirably adjusted by a remote-controllable variable throttle valve provided on the way of a discharge oil passage extending from the hydraulic pump, so that a simple hydraulic circuit is used to make the coupling of two rotary shafts freely adjustable from loose condition to tight condition.