This control apparatus estimates a full combustion correspondence period CP, which is the period from an ignition timing SA to a combustion completion time CAe, and controls a VVT advancement amount (burnt gas quantity, overlap period, intake valve open timing) such that the estimated full combustion correspondence period CP coincides with a constant target full combustion correspondence period CPtgt. The full combustion correspondence period CP substantially maintains a one-to-one relation with the VVT advancement amount at which HC, CO2, etc. start to increase, even when the ignition timing SA changes. Thus, even when the ignition timing changes, the burnt gas quantity (overlap period) can be properly controlled. As a result, without increasing the discharge quantities of HC and CO, the discharge quantity of NOX can be reduced. In addition, pumping loss can be reduced, whereby fuel consumption can be improved.