The present invention discloses a power-on circuit of a peripheral component, which comprises a switch control circuit for controlling the enabling time of a P-type or N-type transistor. For a P-type transistor, the switch control circuit includes a pull-high element, a current source and a current switch. For a N-type transistor, the switch control circuit includes a pull-down element, a current source and a current switch. The enabling time of the P-type or N-type transistors are controlled by the switch control circuit and the capacitor shunt with the switch control circuit so as to slowly enable the transistor switch. In other words, the present invention uses the slowly increasing or decreasing characteristic caused by charging the capacitor with the current source to control the P-type or N-type transistor switch so as to obtain the purpose of slowly enabling the power supply. For designing an IC, it is easy to design a constant current source, which occupies only little area, and the disadvantage of the prior art is thereby resolved.