The stop-start control apparatus (20) is applied to the spark ignition type internal combustion engine (1), stops the internal combustion engine 1 in a case that a prescribed stop condition is fulfilled, and restarts the internal combustion engine (1) in a case that a prescribed restart condition is fulfilled. The control apparatus cuts spark ignition for the internal combustion engine 1 in response to the fulfillment of the stop condition, and carries on fuel supply to the internal combustion engine (1). When a restart condition is fulfilled after the fulfillment of a stop condition and prior to a complete stop of the internal combustion engine (1), the control apparatus restarts the internal combustion engine (1) by resuming spark ignition for the internal combustion engine (1) in order that fuel supplied after the fulfillment of the stop condition burns.