An engine 1 provided with a fuel injection mechanism (a fuel injection system 18 and an FI control unit 41) that supplies fuel of arbitrary quantity into a combustion chamber 9 and a variable valve mechanism (an intake valve 14, an exhaust valve 15, hydraulic electromagnetic valve drive units 16, 17 and a valve event control unit 40) that varies the ratio of burned gas and air-fuel mixture in the combustion chamber 9 for combusting fuel by compression self ignition, is controlled so that a deviation ΔT between combustion initiation temperature and peak temperature after combustion in the combustion chamber 9 is converged in a predetermined range.