A control apparatus operates a compression ignition internal combustion engine by switching between spark ignition combustion using an ignition device and compression ignition combustion which self-ignites a mixture by piston compression. Variable valve mechanisms vary at least one of the valve timings and valve lifts of an intake valve and an exhaust valve. Intake air is regulated to vary the amount of air intake into a combustion chamber on the upstream side of a combustion chamber inlet of the compression ignition internal combustion engine. The variable valve mechanisms and the intake air regulation are controlled during the compression ignition combustion so as to perform the compression ignition combustion.