In order to set with a high precision the value of rush current flowing in the power switch circuit at the time of turning "on" the power, the internal circuit Int_Cir of the LSI is supplied with the internal source voltage Vint from the output transistor MP1 of the regulator VReg of the power switch circuit PSWC. The power switch circuit PSWC includes a control circuit CNTRLR and a start-up circuit STC. During the initial period Tint following the turning "on" of the power supply, the start-up circuit STC controls the output transistor MP1 and reduces the primary rush current so that the output current Isup of the output transistor MP1 may represent an approximately constant increment as the time passes. The difference .DELTA.V between the internal current voltage due to the charge of load capacitance C with the output current Isup controlled by the start-up circuit STC and the current voltage Vint from the regulator VReg is set within the predetermined limit to reduce the secondary rush current.