An apparatus power restart method in response to the network connection status is provided. The method uses an outlet or an Uninterruptible Power Supply (“UPS”) with multiple sockets, wherein a network port and a power reset switch are included. The outlet or UPS is powered via an external power source. A network connection is established through one or more network devices. The electric power control apparatus incorporating the claimed power restart method includes a network connection detection circuit and an electric power control circuit. By monitoring the network connection, the network devices connected to the electric power control apparatus can be restarted in sequence or simultaneously when the network connection fails. Thereby the network connection can be maintained. Additionally, the electric power control apparatus has a server module whereby the users can access the apparatus via the network connection. This allows the user to configure the apparatus.