an abnormality detection apparatus includes : an air / fuel ratio control portion that performs a control of fluctuating the air / fuel ratio between rich and lean states ; a data acquisition portion that acquires , as data for detecting abnormality , a parameter that corresponds to responsiveness during change of output of the a / f sensor between rich and lean peaks during the control ; a straight line setting portion that sets a straight line that represents a tendency of change of the parameter relative to change in intake air amount of the engine based on the data acquired by performing acquisition of the data a plurality of times ; and an abnormality determination portion that determines the presence / absence of abnormality of the a / f sensor based on comparison between the gradient of the set straight line and an abnormality criterion value .