A method of operating a hydrogen generator includes: a step (a) of generating a hydrogen-containing gas by a hydrogen generation unit by using a raw material in the hydrogen generation unit; a step (b) of removing a sulfur compound from the raw material by a hydrodesulfurizer which is heated by heat transferred from the hydrogen generation unit; and a step (c) of performing an operation of supplying the raw material to the hydrogen generation unit after stopping the generating of the hydrogen-containing gas by the hydrogen generation unit. The step (c) is not performed unless, at least, a temperature of the hydrodesulfurizer is such a temperature at which carbon deposition from the raw material is suppressed.