In view of a difference in detectability of an air-fuel ratio sensor with respect to each cylinder, a first exhaust system model and a second exhaust system model are defined. The first exhaust system model outputs an air-fuel ratio at the confluent portion based on an air-fuel ratio in a cylinder. The second exhaust system model outputs a detection value of the exhaust gas sensor based on the air-fuel ratio at the confluent portion. A confluent-portion-air-fuel ratio estimating portion designed based on the second exhaust system model estimates the air-fuel ratio at the confluent portion. A combust-air-fuel ratio estimating portion designed based on the first exhaust system model estimates a combust-air-fuel ratio in each cylinder.