It is challenging to realize the quantum anomalous Hall effect (QAHE) at high operating temperatures using the two-dimensional (2D) Dirac surface states of three-dimensional (3D) topological insulators (TIs). Given the small non-trivial gap induced by adsorbing ferromagnetic (FM) CrI3 monolayer (ML) on the surface of Bi2Se3 films, we here propose another TI and FM semiconductor interfaced system to enhance the gap by inserting CrI3 ML between the first top (bottom) quintuple layers (QL) and sub-top (sub-bottom) QL of Bi2Se3 films symmetrically. The 2D non-trivial phase emerges in the Bi2Se3 films with five or more QLs and the gap is enlarged to 30 meV in 1QL-Bi2Se3/CrI3/4QL-Bi2Se3/CrI3/1QL-Bi2Se3, which can be understood by the enhanced magnetic proximity effect. The topological non-triviality is confirmed by the nonzero Chern number and the existence of chiral edge state. Our finding will provide useful guidance to optimize the Bi2Se3–CrI3 interface system for realizing QAHE at relatively high operating temperatures.