Water replenishment control method and device and water heater

The invention discloses a water replenishment control method and device and a water heater. The water replenishment control method comprises the steps that the current water temperature of a water tank is detected; a first preset temperature and a second preset temperature are obtained, wherein the first preset temperature is lower than the second preset temperature; when water in the water tank is in the medium water level, according to the relation among the current water temperature, the first preset temperature and the second preset temperature, water replenishment is controlled to be carried out on the water tank based on a preset water replenishment strategy till the water in the water tank is in the high or low water level. By means of the water replenishment control method and device, the technical problem that an existing water heater cannot stably supply hot water is solved.