To control the concentration of NOx appropriately in executing the internal exhaust gas re-circulation by the continuous lift quantity adjustment of an intake valve and an exhaust valve with a cam in an internal combustion engine capable of stratified combustion.

After a first slide correction quantity is calculated so that the actual intake pressure is the target intake pressure, the difference in the air-fuel ratio ΔAF is calculated (S308) based on the difference in the intake pressure ΔPM (S306) generated from whether the internal EGR is executed or not, then the actual internal exhaust gas re-circulation rate egrl is obtained (S310, S312). The actual internal exhaust gas re-circulation rat egrl and the target internal exhaust air re-circulation rate egrt are compared (S314, S316), and an appropriate second slide correction quantity vadjb can be calculated (S318, S320). As the error in the internal exhaust air re-circulation rate is appropriately compensated in this way, the concentration of NOx is appropriately controlled.