An abnormality diagnostic device for an air-fuel ratio sensor that detects the air-fuel ratio of exhaust gas of an internal combustion engine is provided. The abnormality diagnostic device includes: a device that an device that models a system extending from a fuel injection valve to the air-fuel ratio sensor by using a first order response delay element and a waste time element, and that identifies at least a waste time of the waste time element based on an input given to the air-fuel ratio sensor and an output obtained from the air-fuel ratio sensor; and another device that performs determination about an abnormality of the waste time based on the identified waste time.