An apparatus for diagnosing an engine including a variable compression ratio apparatus according to an exemplary embodiment of the present invention, may include a piston configured to reciprocally move in a cylinder of the engine, a detector configured to determine a position of the piston, a variable compression ratio apparatus configured to adjust a moving range of the piston, and a controller configured to determine whether the variable compression ratio apparatus is defective based on a position signal of the piston determined by the detector.