An LED load driving apparatus including a power conversion circuit and a control chip is provided. The power conversion circuit receives an input voltage and drives an LED load in response to a PWM signal. The control chip includes a control core circuit and a memory unit. The control core circuit is operated under a system voltage to provide the PWM signal for controlling operation of the power conversion circuit. The control core circuit is inactivated during a power-off period and restarted during a power-on period. The memory unit is operated under the input voltage and is configured to: store a dimming operation data before the control core circuit is inactivated during the power-off period; and provide the stored dimming operation data during the power-on period to the control core circuit, so as to make the control core circuit perform corresponding dimming operation relating to the LED load.