The invention belongs to the technical field of gas water heaters and discloses an electrically auxiliary preheating circulation gas water heater, a preheating circulation system and a control method.According to the electrically auxiliary preheating circulation gas water heater, a water outlet pipeline is provided with an intelligent heating module connected to a controller, after a preheating circulation function of the gas water heater is started, if the temperature of water heated by the minimum heat load of the gas water heater is higher than the set water outlet temperature Ts, the controller stops gas heating and controls the intelligent heating module to start, and the water is heated to the set water outlet temperature Ts. Through the gas water heater, when the water is heated with gas by the minimum heat load, if the temperature of the heated water is still higher than the set water outlet temperature, gas heating can be stopped, heating is conducted through the intelligentheating module till water is heated to the needed set water outlet temperature, and the requirements that on the premise that zero cold water is achieved, the problem of uneven water outlet temperatures is avoided, a user does not need to draw off water to wait for hot water, and hot water is available at any time are met.