A method for operating a polymer electrolyte membrane fuel cell at temperatures below the freezing point of water and an apparatus thereof are provided to prevent damage and performance degradation of the membrane-electrode assemblies. Non-humidified gas flows for several seconds before temperature of the polymer electrolyte membrane fuel cell falls below the freezing temperature of water when operation of the polymer electrolyte membrane fuel cell stops. Simultaneously, anode of the polymer electrolyte membrane fuel cell is filled with a solution having a low freezing point to prevent the temperature of a polymer electrolyte membrane fuel cell falling below the freezing point of water due to the lower ambient temperature in the winter. When the polymer electrolyte membrane fuel cell is restarted, the cell performance is not degraded reflecting that the present invention stably preserves the fuel cell.