As an important aspect of inclusion engineering, numerical prediction of inclusion behavior in molten steel has attracted much attention in order to control inclusions in steel. Although considerable efforts have been made in the modeling of inclusion growth, it is still necessary to employ an initial particle size distribution (PSD) gained from experiments or assumptions as an input for numerical models. The present work focuses on the construction of a general nucleation-growth model, which combines thermodynamics, classical homogeneous nucleation theories and dynamics of particle collision and coagulation on the basis of mean processing parameters. This can be employed, without any initial PSD of inclusions in advance, to describe the time evolution of PSD in molten steel during inclusion nucleation, Ostwald ripening, and collision growth processes. With regard to collision-coagulation growth mechanisms of inclusions, four approaches, namely Brownian collision, turbulent collision, Stokes collision and gradient collision in laminar shear layers, have been investigated to estimate their role in the evolution of PSD during steel melt deoxidation process. In addition, an approximate numerical technique, termed the ‘DS method’, has been developed as a modification of the so-called (1) discrete-sectional representation and (2) Particle-Size-Grouping method in order for an efficient solution for population balance equations (PBE) at lower cost in CPU time. Finally, as an application of this general model, the evolution of nucleation and growth of alumina inclusions is demonstrated in the Fe-Al-O melt system. The predicted molten steel total oxygen and particle size distribution of alumina inclusions are compared with the experiment data cited from references.