(57) In an NO_x generation quantity estimation method for an internal combustion engine, the concentration of a gas contained in intake gas and serving as a material for generation of NO_x, (intake-gas oxygen concentration), a load index value indicating the load of the engine (fuel injection quantity), an atomization index value indicating the degree of atomization of fuel within the combustion chamber (fuel injection pressure), and the highest flame temperature are selected as peripheral condition quantities in relation to gas mixture which affect the quantity of NO_x generated in a combustion region as a result of combustion. A combustion-generated NO_x quantity per unit fuel quantity (combustion-generated NO_x ratio) is obtained on the basis of the four peripheral condition quantities and a predetermined empirical formula which defines the relation between the four peripheral condition quantities and the combustion-generated NO_x ratio. Subsequently, the quantity of generated NO_x is estimated through multiplication of the combustion-generated NO_x ratio by the fuel injection quantity.