The invention relates to a control method of a gas water heater and the gas water heater. The gas water heater comprises a gas heating unit. The gas heating unit communicates with a water inlet pipe and a water outlet pipe. An electric heater used for conducting fast heating on inlet water is arranged on the water inlet pipe. When the water inlet temperature of the gas water heater is smaller than the set value, the electric heater on the water inlet pipe is started to conduct fast heating on the inlet water, the operating power of the electric heater is adjusted according to the water inlet temperature detection value and/or the water outlet temperature detection value, and accordingly, the water outlet temperature reaches the set value. Through the arrangement and the control method, the purposes that the electric heater is automatically controlled, and auxiliary electric heating is conducted on water flowing through the water inlet pipe are achieved, the water inlet temperature of the gas water heater is remarkably increased, the power of the gas water heater is improved, and the application environment of the gas water heater is broadened. Meanwhile, the gas water heater is simple in structure, the control method is concise, the effect is remarkable, and the control method of the gas water heater and the gas water heater are suitable for application and popularization.