A heater control device of an oxygen concentration sensor is provided in which even in a case where an internal combustion engine is automatically stopped by idle stop control after cold start-up, it is possible to start energization of a heater at an appropriate time.The heater control device includes a model temperature calculation section that calculates model temperature around the oxygen concentration sensor, a heat amount integration section that calculates an integrated heat amount by integrating the amount of heat passing through an installation position of the oxygen concentration sensor, an energization instruction section that starts the energization of the heater when the integrated heat amount has reached a predetermined energization start threshold value, a reset section that resets the integrated heat amount and the energization start threshold value at the time of stop or start-up of the internal combustion engine and, on the other hand, does not reset the integrated heat amount and the energization start threshold value at the time of automatic stop and restart of the internal combustion engine by the idle stop control, and a correction section that corrects the integrated heat amount or the energization start threshold value in consideration of the influence of heat radiation during the automatic stop of the internal combustion engine by the idle stop control.