The objective of the present invention is to provide a control device for an engine that enables precise control of the equivalence ratio. The system from the fuel injection amount to the output from a LAF sensor is modeled as an injection amount-sensor output model by means of a model equation containing model parameters and a lag coefficient. The system from the equivalence ratio to the LAF sensor output is modeled as a port equivalence ratio-sensor output model by means of a model equation containing the lag coefficient. The control device is equipped with: a feedback-use identifier that successively identifies values for the model parameters; a LAF lag compensation-use identifier that successively identifies values for the lag coefficient; and a stoichiometric driving mode controller that determines the value of a fuel injection amount.