An internal EGR parameter estimating device is configured to estimate the internal EGR quantity based on the quantity of blow-by gas that blows by during an overlap period when both the intake valve(s) and the exhaust valve(s) are open. The blow-by gas quantity is calculated based on the intake air pressure and the exhaust gas pressure during the overlap period and the effective cross sectional area opening formed by the intake and exhaust valves. The overlap period is divided into intervals of a prescribed period and the interval cross sectional area opening during each interval is calculated.