Abstract Complex TiN + oxide inclusions which nucleate and grow on the surface of the primary oxide inclusions, e.g. MgO, have been frequently observed in various steel grades after solidification. To describe the precipitation kinetics of TiN and TiN + MgO inclusions, a model accounting for both heterogeneous and homogeneous nucleation was proposed in this work. The model was validated by employing the literature data, and good agreement has been achieved between experimental data and calculation data. The influence of nitrogen and titanium concentrations, the interfacial tension between TiN and steel, cooling rate, and size distribution of primary oxides on the size distribution of TiN and TiN + MgO inclusions were investigated by the model calculations. It was found that nitrogen and titanium concentrations, the interfacial tension between TiN and steel, and the number density of primary MgO inclusions have an impact on the final size distributions of TiN and TiN + MgO inclusions. In contrast, the effects of cooling rate and size of MgO inclusions on the final inclusion size distribution are negligible. The large interfacial tension between TiN and steel would suppress the homogeneous nucleation and is favorable to heterogeneous nucleation. The increase of the number density of primary MgO can significantly suppress the homogeneous nucleation and reduce the size of TiN + MgO inclusions. The present model can be extended to describe the heterogeneous precipitation of other complex inclusions providing that the secondary inclusion has a low lattice mismatch with the primary inclusion. Combining the present model with our previous model for the size distribution of primary inclusions, the size distribution of inclusions in solidified steel can be well described and controlled.