A power transmission system transmits power from a drive shaft of an internal combustion engine to a first and a second auxiliary device through a belt. An auto-tensioner extends or contracts to change the tension of the belt. A controller rotates the first auxiliary device in a reverse direction to loosen the belt to cause the auto-tensioner to extend to increase the tension of the belt and calculates a reversing timing when the drive shaft will be reversed as a result of increasing of the tension of the belt. The controller inhibits the tensioner body from contracting immediately before or when the reversing time is reached to keep the tension of the belt at an increased degree, thereby eliminating the slippage of the belt on each pulley without having to finely control the operation of the first auxiliary device when the internal combustion engine is started.