A hydraulic system for an automatic transmission of a motor vehicle, with which hydraulic cylinders of at least one clutch, and of gear selectors can be actuated, which hydraulic system includes a pressure accumulator for providing an accumulator pressure in the hydraulic system. In at least one clutch path leading from the pressure accumulator to the clutch hydraulic cylinder, a clutch valve, which can be operated by an electronic control unit, and with which a hydraulic pressure applied to the clutch hydraulic cylinder can be adjusted, and a pressure sensor, with which the hydraulic pressure applied to the clutch hydraulic cylinder can be detected, are arranged, and having a charging hydraulic pump, which delivers hydraulic fluid into the hydraulic system in a charging process to increase the actual accumulator pressure.