A hydraulic system for an automatic transmission of a motor vehicle, with which the hydraulic cylinders of at least one clutch and of gear selectors can be actuated, which hydraulic system has a pressure accumulator for providing an accumulator pressure in the hydraulic system. A gear selector valve that can be controlled by an electronic control unit is arranged in at least one gear selector path leading from the pressure accumulator to the gear selector hydraulic cylinder, with which valve the hydraulic pressure at the gear selector hydraulic cylinder can be adjusted, and a charging hydraulic pump which conveys hydraulic fluid into the hydraulic system in a charging process, in order to increase an accumulator pressure in the hydraulic system.