A liquid heater apparatus increases the temperature of an A/F sensor up to a target temperature by a target heating time. The liquid heating apparatus such as a gas water heater uses the A/F sensor for detecting an oxygen density in a heating tube. An MPU of a controller count a time from beginning by using a timer and decides whether a moisture on the A/F sensor is evaporated by using the change of a current for a heater portion of the A/F sensor. When the MPU decides the A/F sensor is dried out, the MPU counts the time from the beginning to such time tα as a drying time and setts a heating completing time by reducing the drying time from the predetermined target time. The MPU so controls the heating portion that the temperature of the sensor portion becomes the target temperature by the heating completing time.