An apparatus for diagnosing a failure of a sensor may include an engine; an intake manifold; a turbocharger including a turbine rotated by exhaust gas of the combustion chamber and a compressor provided at the intake line, rotated in connection with the turbine, and compressing external air; a map sensor measuring a pressure of a front end portion of the compressor; a differential pressure sensor measuring a differential pressure of front and rear end portions of an EGR valve provided at an EGR apparatus; an operation information detecting device measuring operation information including an engine speed and a load; and a controller determining whether an exhaust gas pressure is constant from the operation information and comparing a change amount of the differential pressure sensor signal and a change amount of the map sensor signal in the condition that the exhaust gas pressure is constant to diagnose a failure of the differential pressure sensor.