There are arranged an engine 10 having idle-stop control means and an automatic transmission 20 having as a hydraulic-pressure supply source a main pump 22 driven by the engine 10 to perform speed change control. There are arranged a bypass hydraulic passage 45 for ensuring communication between said main pump 22 and a point immediately before an engagement-pressure supply port of a forward engagement element L/C in the automatic transmission, a switching valve 44 on the bypass hydraulic passage 45 for allowing switching between the communicating state and the non-communicating state, and switching-valve control means for switching the switching valve 44 between the communicating state and the non-communicating state. With this, the main pump is stopped at idle-stop control to supply the hydraulic pressure required for restart, allowing smooth running.