The invention discloses a filter screen cleaning reminding method which includes the steps: starting timing and recording the working time of the water heater for heating by air energy when detecting that the water heater starts heating by the air energy; acquiring accumulated time in timing record to obtain the sum of the working time and the accumulated time; outputting cleaning reminding signals of a filter screen when the sum of the working time and the accumulated time is longer than preset time. The invention further discloses a water heater and a computer readable storage medium. The water heater can remind a user of cleaning the filter screen in more appropriate time, the filter screen can be timely cleaned, output of the cleaning reminding signals can be prevented when the filter screen does not need cleaning, the user is prevented from consuming a large amount of time for frequently cleaning the filter screen, normal operation of the water heater is ensured, and good experience of the user is ensured.