The constant current circuit includes a constant current generation circuit, a start-up detection circuit configured to detect start-up of the constant current generation circuit, and a clamp circuit configured to output a start-up voltage to the constant current generation circuit. The start-up voltage output from the clamp circuit is a voltage close to gate voltages that are higher than gate voltages of transistors that form a current mirror circuit of the constant current generation circuit, in a state where the constant current generation circuit is operating.