The invention provides an ignition combustion engine by the mode of mixing hydrogen and oxygen with high-octane fuel and a control method thereof, and particularly relates to a fuel storage and supply system of the ignition combustion engine by the mode of mixing the hydrogen and the oxygen with the fuel, fuel proportional distribution and combustion process control, wherein, a set of on-board hydrogen and oxygen production, a storage and supply device is added to the system on the basis of retaining main parts and an electronic control unit of the original engine. The hydrogen and oxygen mixed fuel electronic control unit (12) can control the opening and closing of a hydrogen nozzle and an oxygen nozzle according to sensor signals c-h so that the engine can run in three combustion modes such as pure hydrogen and oxygen mixed gas, hydrogen-oxygen-high-octane fuel mixed gas and pure high-octane fuel according to different operating conditions, thus greatly lowering HC and CO emission in the case of cold starting and idling of the high-octane fuel combustion engine and improving the thermal efficiency and emission level of the high-octane fuel combustion engine in middle and low load stages.