To permit coping with the fluctuation of hot-water supplying demand optimally by a method wherein a waste heat recovery means with additional heating function for recovering the waste heat of a power generating means is provided while the additional heating function is operated when a hot-water discharging temperature is lower than a predetermined value and the flow rate of a water outlet pipe is higher than a predetermined value to switch high-temperature water, generated by the recovery of waste heat, into a bypass pipeline.

In a hot-water storage type electric water heater, equipped with a water supplying pipe 3 for supplying water into a hot-water storage tank 2A and a water outlet pipe 4 for supplying hot-water heated in an electric heater 5, the waste heat of a gas engine generator 10 is recovered by a waste heat recovering device 20 to charge a part of the recovered waste heat into the hot-water storage tank 2A by a waste heat charging means A including a heat exchanging unit 21. In this case, when a hot-water discharging temperature is decided that it is lower than a predetermined value and the flow rate of the water outlet pipe 4 is decided that it is higher than a predetermined value by the signals of a temperature sensor S1 and a flow rate sensor S2 in a control unit CU, a proportional control valve V1 is controlled to control a bathtub water reheating burner 11. At the same time, pipeline is switched into a bypass pipeline L3 by controlling a three-way valve V2 to guide high- temperature water into the water outlet pipe 4 and prevent the depletion of supply of hot-water.