In a constant current switching power supply, the current flowing through the load, is feedback-controlled based on the deviation of the detection value (Id) from the target value (Ir), multiplied by a proportional gain (PG), the value of the gain is set to a predetermined value immediately after the load switching element (5) is turned on, and is thereafter gradually reduced with elapse of time. When the current to the load (4) is supplied by a PWM controlled switching circuit (1), the PWM signal is determined based on a product of the deviation and a proportional gain. It is possible to shorten the rise time of a pulsative load current in a situation where the current is relatively large.