Two heterostructures consisting of a Bi ₂ Se ₃ topological insulator substrate and a CrI ₃ or CrBi ₂ Se ₄ ferromagnetic insulator thin film have been theoretically studied. The calculated band structure indicates that both heterostructures exhibit the quantum anomalous Hall effect with the splitting of the topological surface state of 19 and 92 meV for CrI ₃ /Bi ₂ Se ₃ and CrBi ₂ Se ₄ /Bi ₂ Se ₃ , respectively. It has been shown that the band gap is determined primarily by the degree of localization of the wavefunction of the topological state in the ferromagnetic film. This degree of localization depends on the height and width of the interface barrier between the substrate and ferromagnetic material. Both the height and width of the interface barrier in the CrBi ₂ Se ₄ /Bi ₂ Se ₃ system are similar to the respective characteristics of the van der Waals barrier in bulk Bi ₂ Se ₃ .