A load driving apparatus relating to light-emitting-diodes (LEDs) is provided. In the invention, a compensation voltage on a compensation pin (CMP) of a control chip does not change in response to (or with) the variation (i.e. enabling and disabling) of a pulse-width-modulation (PWM) signal for dimming. In other words, regardless of whether the PWM signal for dimming is enabled or disabled, the compensation voltage on the compensation pin of the control chip maintains unchanged. Therefore, an LED string at the current switching transient does not have the generation of over-shoot current. Furthermore, by detecting the compensation voltage on the compensation pin of the control chip, the control chip would enter into a shutdown status in response to the detected compensation voltage being greater than a predetermined threshold voltage for a predetermined counting time in case that the LED string is failure.