A control system includes a controller. The controller estimates the swing-back amount indicating the turning amount of the crankshaft in the reverse rotation direction until the crankshaft stops. The controller calculates a stop-time counter value which is a value of a crank counter at the time when the engine is stopped based on a final counter value which is the value of the crank counter calculated last before the crankshaft stops and the estimated swing-back amount. The controller corrects the swing-back amount used for calculating the stop-time counter value based on a difference between the number of driving times calculated with reference to the map based on the calculated stop-time counter value and the value of the crank counter and the number of driving times calculated by increasing the number of driving times by one each time the high pressure system fuel pressure increases by the threshold or more.