The invention discloses a heat exchanger of a gas water heater and the gas water heater. The heat exchanger of the gas water heat comprises a heat exchange structure which comprises a plurality of heat exchange fins, heat exchange pipes which string the heat exchange fins and U-shaped pipes communicating all the heat exchange pipes. The heat exchanger further comprises a heat insulating layer located between the heat exchange structure and a combustor of the gas water heater and surrounding the periphery of a combustion chamber of the gas water heater, the upper end of the heat insulating layer is connected with the lower end of the heat exchange structure, and a gap is reserved between the lower end of the heat insulating layer and the combustor of the gas water heater. The heat exchanger of the gas water heater and the gas water heater simplifies the structural design of the heat exchanger, reduces the usage amount of copper materials and therefore reduces the production cost. In addition, heat conduction and heat radiation loss of high-temperature flue gas in the combustion chamber can be reduced, and the heat exchange efficiency of the heat exchanger is effectively improved.