To avoid the occurrence of knocking and reduction in torque at high load operation time even if the compression ratio is set high for obtaining compression ignition combustion.

The valve timing is variably set with every operation area, and four-cycle compression ignition combustion is performed in a low-medium rotation and low load area (a). While two-cycle spark ignition combustion is performed in a low-medium rotation and high load area (b), four-cycle spark ignition combustion is performed in a high rotation area (c). A negative overlap period for closing both suction and exhaust valves is formed before and after the exhaust upper dead center in the four-cycle compression ignition combustion, residual gas is shut in, intake air is heated and raised in the temperature by this residual gas, and a gas temperature in a combustion chamber is enhanced up to a self-ignitable temperature by adiabatic combustion. The actual compression ratio is reduced in the two-cycle spark ignition combustion to avoid the occurrence of the knocking and reduction in the torque. Miller cycle operation is performed in the four-cycle spark ignition combustion to avoid the occurrence of the knocking and reduction in the torque.