In a multi-stage fuel-injection internal combustion engine employing a fuel injection system and a variable valve actuation system, engine valve timings are variably controlled depending on engine operating conditions. An electronic engine control unit is configured to execute cooperative control of the timing of sub-injection, injected before main injection, responsively to intake valve closure timing, and also to execute cooperative control of the timing of sub-injection, injected after the-main injection, responsively to exhaust valve open timing.