An internal combustion engine is operated on auto-ignition combustion of fuel with low cetane number like gasoline. The engine has at least one cylinder and a reciprocating piston in the cylinder to define a combustion chamber. Combustion event in the cylinder is expressed in terms of two variables. They are main combustion timing (&thgr;50) and a main combustion period (&thgr;20-50). The main combustion timing (&thgr;50) represents a crank position when mass burnt rate is 50 percent. The main combustion period (&thgr;20-50) represents a period from a crank position when mass burnt is 20 percent to a crank position when mass burnt is 50 percent. Controlled parameters governing main combustion are varied to adjust the main combustion timing on an advance side of a retard limit (&thgr;50 max) and to adjust the main combustion period within a range between an upper limit (&thgr;20-50 max) and a lower limit (&thgr;20-50 min).