A prescribed threshold level Dth for misfire judgment for each cylinder is recorded in a misfire judgment level retaining means 102 of a misfire judgment processing section 100. A combustion state parameter operation means 106 measures revolution speed of a multi-cylinder engine for each cylinder, and attains as a combustion state parameter a differential in revolution speed between a specific cylinder and other cylinders. In a misfire judgment level correction means 104, a plurality of combustion state parameters concerning the specific cylinder is attained, and the above-mentioned threshold level Dth is corrected as a function of the parameter. A misfire judgment processing means 108 compares the combustion state parameter with the threshold level Dth and diagnoses a combustion state in the specific cylinder. Namely, the corresponding cylinder is judged to be misfire when the combustion state parameter of the specific cylinder exceeds the prescribed parameter.