A CPU substitutes a difference between a crank-side speed that is a rotation speed of a crankshaft and a downstream-side speed that is a speed of a portion, opposite from the crankshaft, in a damper into a differential speed. The CPU calculates a torsion angle through a process of integrating the differential speed. The CPU calculates a torsion speed component that is a speed component of the crankshaft due to torsion of the damper based on a process of integrating a value obtained by multiplying the torsion angle by an elastic modulus, and calculates a time that is a variable indicating a speed of the crankshaft, used to determine a misfire, based on the torsion speed component. The CPU subtracts a value obtained by subtracting an output value of the integrating process, applied to a finite response low-pass filter process, from the output value.