A controller of an air-fuel-ratio sensor according to an embodiment includes a current supplying unit, a sweep processing unit, and an abnormality detecting unit. The current supplying unit supplies a current to the pump cell through a first terminal connected with the pump cell so as to control the pump cell. The sweep processing unit executes a sweeping process in which a predetermined voltage or a predetermined current is applied to the detection cell through a second terminal connected with the detection cell so as to change a voltage and a current of the detection cell. The abnormality detecting unit detects a short-circuited state between the first terminal and the second terminal on the basis of a fluctuation in a voltage or a current, generated by the sweeping process, of the first terminal.