A network wake up system includes a network card, a controller, a south bridge chip, and a baseboard management controller (BMC). The network card receives a network wake up data packet, and outputs a network wake up signal. The BMC determines whether a temperature of the computer is in a predetermined temperature range and determines whether a voltage of the computer is normal, and outputs a state signal to the controller. If the temperature of the computer is in the predetermined temperature range and the voltage of the computer is normal, the controller wakes up the computer at the power-off state. If the temperature of the computer is not in the predetermined temperature range or the voltage of the computer is abnormal, the controller fails to output the network wake up signal to the south bridge chip, so that the computer at the power-off state cannot be woken up.