A control system of a compression ignition type internal combustion engine comprising a fuel injector arranged in a combustion chamber and an electronic control unit controlling a fuel injection action from the fuel injector, a main injection fuel injected from the fuel injector being ignited by a premixed charge compression ignition, wherein said electronic control unit is configured to start an injection of the main injection fuel from the fuel injector within a range of crank angle from 10 degree before the compression top dead center to 10 degree after the compression top dead center and make a smaller amount of auxiliary injection fuel than the main injection fuel be injected from the fuel injector before the main injection fuel to ignite the auxiliary injection fuel by the premixed charge compression ignition, and said electronic control unit is further configured to control an injection timing of the auxiliary injection fuel to an injection timing whereby the premixed charge compression ignition of the main injection fuel is caused by a heat generated by the premixed charge compression ignition of the auxiliary injection fuel after a start of injection of the main injection fuel; characterized in that: a target compression ignition timing of the auxiliary injection fuel for causing the premixed charge compression ignition of the main injection fuel at a predetermined timing is set in advance between a time of the completion of injection of the main injection fuel and the compression top dead center or between a time of the start of injection of the main injection fuel and a time of the completion of injection of the main injection fuel; said electronic control unit is configured to control the injection timing of the auxiliary injection fuel to an injection timing at which the premixed charge compression ignition timing of the auxiliary injection fuel becomes said target compression ignition timing; and the injection timing of the auxiliary injection fuel is advanced proportionally to an increase of the engine speed so that a rate of a premixed charge with an equivalent ratio of 1.0 to 2.0 in a premixed charge generated by the auxiliary injection fuel becomes maximum at said target compression ignition timing. said electronic control unit is configured to start an injection of the main injection fuel from the fuel injector within a range of crank angle from 10 degree before the compression top dead center to 10 degree after the compression top dead center and make a smaller amount of auxiliary injection fuel than the main injection fuel be injected from the fuel injector before the main injection fuel to ignite the auxiliary injection fuel by the premixed charge compression ignition, and said electronic control unit is further configured to control an injection timing of the auxiliary injection fuel to an injection timing whereby the premixed charge compression ignition of the main injection fuel is caused by a heat generated by the premixed charge compression ignition of the auxiliary injection fuel after a start of injection of the main injection fuel; characterized in that: a target compression ignition timing of the auxiliary injection fuel for causing the premixed charge compression ignition of the main injection fuel at a predetermined timing is set in advance between a time of the completion of injection of the main injection fuel and the compression top dead center or between a time of the start of injection of the main injection fuel and a time of the completion of injection of the main injection fuel; said electronic control unit is configured to control the injection timing of the auxiliary injection fuel to an injection timing at which the premixed charge compression ignition timing of the auxiliary injection fuel becomes said target compression ignition timing; and the injection timing of the auxiliary injection fuel is advanced proportionally to an increase of the engine speed so that a rate of a premixed charge with an equivalent ratio of 1.0 to 2.0 in a premixed charge generated by the auxiliary injection fuel becomes maximum at said target compression ignition timing. a target compression ignition timing of the auxiliary injection fuel for causing the premixed charge compression ignition of the main injection fuel at a predetermined timing is set in advance between a time of the completion of injection of the main injection fuel and the compression top dead center or between a time of the start of injection of the main injection fuel and a time of the completion of injection of the main injection fuel; said electronic control unit is configured to control the injection timing of the auxiliary injection fuel to an injection timing at which the premixed charge compression ignition timing of the auxiliary injection fuel becomes said target compression ignition timing; and the injection timing of the auxiliary injection fuel is advanced proportionally to an increase of the engine speed so that a rate of a premixed charge with an equivalent ratio of 1.0 to 2.0 in a premixed charge generated by the auxiliary injection fuel becomes maximum at said target compression ignition timing.