A failure detection apparatus for a resolver outputting a sine signal indicative of sin θ and a cosine signal indicative of cos θ according to a rotational angle θ of a rotator, includes an inspection value calculating section configured to calculate an inspection value based on at least one of the sine signal and the cosine signal; a failure detecting section configured to judge whether the resolver is in a failure state or not on the basis of the inspection value; a counting section configured to gradually increase a count value with a lapse of time when the failure detecting section is determining that the resolver is in the failure state, and configured to gradually decrease the count value with a lapse of time when the failure detecting section is determining that the resolver is not in the failure state; and a failure deciding section configured to finally decide that the resolver has caused the failure on the basis of the count value.