A control apparatus for a four-stroke premixed compression ignition internal combustion engine opens an exhaust valve to discharge burned gas from a combustion chamber at a first exhaust-valve opening timing, and reopens the exhaust valve at a second exhaust-valve opening timing that is retarded with respect to the intake-valve opening timing. Thus, burned gas discharged from the combustion chamber flows back into the combustion chamber through the exhaust port. The control apparatus retards the second exhaust-valve opening timing as the load on the engine increases. This obviates the need to decrease the lift of the exhaust valve to decrease the amount of burned gas that is reintroduced into the combustion chamber and prevents increases in the resistance against the flow of burned gas into the combustion chamber.