A control apparatus which is capable of enhancing the accuracy of control of a controlled object having characteristics that dead time and response delay thereof vary. The control apparatus includes an ECU. The ECU calculates four predicted values as values of a controlled variable associated with respective times when four dead times elapse, respectively, calculates four weight function values associated with an exhaust gas volume, and calculates four products by multiplying the predicted values by the weight function values, respectively. The ECU sets the total sum of the four products as a predicted equivalent ratio and calculates an air-fuel ratio correction coefficient such that the predicted equivalent ratio becomes equal to a target equivalent ratio.