In a gas hot water heater, changes of the signal output of an A/F sensor are calibrated in the atmosphere, in which the A/F sensor detects an oxygen concentration in a combustion tube. The gas supplied via a gas supply pipe is injected, together with in-taken air, into a combustion tube, which is incorporated in a hot water supply tank, via an injection unit. A proportional valve controls a combustion state in the combustion tube based on the detected oxygen concentration to thereby heat water supplied in the hot water supply tank. A purging process is performed to supply air into the combustion tube, at a timing between an extinguishment operation first performed after the ignition the gas mixture in the combustion tube and a re-ignition operation. Changes of signal output characteristics of the A/F sensor are subject to the calibration after the purging process.