An individual-cylinder air-fuel ratio estimation model is designed so as to consider the mixing of gases exhausted from adjacent combustion cylinders, and a movement by which a mixed gas arrives at the position of an air-fuel ratio sensor, in order that influences ascribable to the intervals (combustion intervals) of the adjacent combustion cylinders may be reflected on the estimation values of individual-cylinder air-fuel ratios. In evaluating the mixing of the gases which are exhausted from the adjacent combustion cylinders, there are considered the lengths and shapes of the exhaust manifolds of the respective combustion cylinders. In evaluating the movement by which the mixed gas arrives at the position of the air-fuel ratio sensor, there are considered a distance or volume from the confluence to the position of the air-fuel ratio sensor, and the exhaust gas quantities of the respective combustion cylinders.