An object of this invention is to promptly detect a crank angle based on in-cylinder pressures and easily compensate for a detection error by processing that has a low computational load. An ECU 50 calculates an in-cylinder pressure ratio (Pn+1/Pn) based on in-cylinder pressures Pn and Pn+1 at two crank angles separated by a predetermined angle Δθ. The ECU 50 includes map data that represents relations between volume ratio parameters (Vnκ/Vn+1κ) calculated using in-cylinder volumes Vn and Vn+1 at the crank angles, and the crank angles. Therefore, when cranking, a crank angle can be detected based on the in-cylinder pressure ratio and the map data earlier than a conventional cylinder discrimination operation. Gains included in the in-cylinder pressures Pn and Pn+1 can be removed by dividing the two pressures, and exponential operations and the like can be eliminated by using the map data to thus suppress the computational load.