When a memory chip is in a standby mode, a ground power supply line of a flip-flop forming a memory cell is intermittently placed in the floating state. A switching NMOS transistor is connected between the ground power supply line and a power supply VSS. The gate of the NMOS transistor is controlled by an activation signal. When entering the floating state, the ground power supply line is charged due to an off-leakage current flowing in the transistor of the memory cell. As a result, the voltage of the ground power supply line is increased from the voltage of the power supply VSS. Accordingly, the off-leakage current of the memory cell is reduced, whereby the standby-time power consumption of the memory chip is decreased. When the voltage of the ground power supply line keeps going up, it becomes impossible to read data held in the memory cell in a short time, resulting in the data being lost. In order to prevent the loss of the data, the switching NMOS transistor is made to intermittently turn on.