A power conversion apparatus includes: a power supply circuit, a load switch and a control circuit. The power supply circuit generates a first power. The load switch controls the power path from the power supply circuit to a load. The control circuit generates a switching control signal to control a conduction level of the load switch according to an enable signal. The control circuit controls a level of the switching control signal to soft start from a first level to a second level. During the soft start period, the switching control signal has plural waveform segments including a first waveform segment and a second waveform segment. A level variation speed of the first waveform segment is higher than a level variation speed of the second waveform segment. The first waveform segment level precedes the second waveform segment level.