In a network hibernation system which comprises a power controller (2) which outputs time-out signal when the event does not occur in the peripheral equipment for sometime; a power supply (3) for backing up of data which outputs a power interruption detection signal when the power supply is cut off with the power supplied urgently by the battery (34) and cuts off the power of battery when the power interruption signal is inputted; a controller (1) which backs up data in network environment and thereafter,outputs the power interruption signal when the power interruption detection signal or the time-out signal is inputted and recovers the data and environment backed up on the memory so that the computer may operate in the same state as the former state; a network interface (4)for the network connection; a supplementary memory (5)in which the data for backing up the hardware state or the working environment are stored in the computer; and a memory (6) in which the hibernation information is stored, and recovers the working environment to the former state when the power is cut off abruptly in the network environment and thereafter, the power is turned on again and also, interrupts the power automatically when the computer is not used for sometime and thereafter, recovers the working environment to the former state when the power is applied again so that the consumed power may be saved, a process comprising the steps of estimating whether the network hibernation is enabled and consequently loading the network hibernation module.