An apparatus for detecting a failure of an exhaust gas sensor disposed in an exhaust manifold is provided. The apparatus comprises a control unit. The control unit compares detection values of the exhaust gas sensor detected under different element temperatures of the exhaust gas sensor. The control unit detects a failure of the exhaust gas sensor based on the comparison result. In one embodiment, the different states include a state in which the element temperature is maintained at higher level and a state in which the element temperature is maintained at lower level. The element temperature can be controlled by a response assignment control scheme. In one embodiment, the detection values are subjected to a filtering process and/or a statistical process using a successive least squares method. The control unit compares the statistically processed detection values to detect a failure of the exhaust gas sensor.