Inoculation is an important method to generate fine equiaxed grain structures in alloys during solidification, which is widely used in shape casting and direct chill casting processes of aluminium alloys. Different from the normal casting processes, welding and additive manufacturing can have ultrahigh cooling rate and temperature gradient during solidification. This makes the grain refinement by inoculation method more difficult. Therefore, a deeper understanding on the influences of cooling rate and temperature gradient on the nucleation and growth of grains is necessary. In this work, a numerical model is developed to quantitatively address the above influences. The model has been successfully applied to predict the grain size in the welding of aluminium alloys as a function of locations.