A load driving apparatus related to an LED lamp and a method thereof are provided. The load driving apparatus includes a PWM-based power converter and a determination circuit. The PWM-based power converter is coupled to the LED lamp, and is configured to: generate a DC operation voltage of the LED lamp; and control a current flowing through the LED lamp in response to a dimming signal, so as to adjust a brightness of the LED lamp. The determination circuit is coupled to the PWM-based power converter and the LED lamp, and is configured to: receive the DC operation voltage; and stop conducting the DC operation voltage to the LED lamp in case that a lamp-off condition of the LED lamp is satisfied.