To provide a variable speed hydraulic system of an automatic transmission capable of accomplishing a smooth start corresponding to an operator's traveling intention when restarting an engine after an idle stop in the variable speed hydraulic system of the automatic transmission using an oil pump driven by the engine as a hydraulic feeding source.

The variable speed hydraulic system has an idle stop control means, and comprises a change-over valve capble of changing over the communication condition of a regular oil passway or a bypass oil passway with a fastening element for forwarding. The variable speed hydraulic system is provided with a target engine speed setting means for setting a target engine speed, in which the fastening pressure of the fastening element for forwarding can be obtained based on a map making oil temperature or a throttle opening or an engine stop time an element, and a change-over control means which outputs a communication demand with the fastening element for forwarding and the bypass oil passway when restarting the engine afte the idle stop, and outputs the communication demand with the fastening demand for forwarding and the regular oil passway.