For the purpose of improving the fuel efficiency by lean combustion and enhancing the fuel efficiency improvement effects by performing compression ignition efficiently in some cylinders, a multi-cylinder spark ignition engine is constructed such that exhaust gas, that is exhausted from preceding cylinders 2A, 2D on the exhaust stroke side among pairs of cylinders whose exhaust stroke and intake stroke overlap in a low load, low rotational speed region, is directly introduced through an inter-cylinder gas passage 22 into following cylinders 2B, 2C on the intake stroke side and only gas exhausted from the following cylinders 2B, 2C is fed to an exhaust passage 20, which is provided with a three-way catalyst 24. Combustion controller is provided that controls the combustion of each of the cylinders such that combustion is conducted by forced ignition in a condition in which the air/fuel ratio is a lean air/fuel ratio which is larger by a prescribed amount than the stoichiometric air/fuel ratio in the preceding cylinders 2A, 2D and, in the following cylinders 2B, 2C, fuel is supplied to burnt gas of lean air/fuel ratio introduced from the preceding cylinders 2A, 2D and combustion is conducted by compression ignition.