The presence of flat mini-bands in moiré materials provides an opportunity to explore correlation effects and topological physics. In this work, we study moiré mini-bands in a topological insulator thin film modelled by two hybridized surface states under a moiré superlattice potential created by another two-dimensional insulating material. We show the lowest conduction (highest valence) Kramers’ pair of mini-bands can be Z­₂ non-trivial when the minima (maxima) of moiré potential approximately form a hexagonal lattice with six-fold rotation symmetry. Coulomb interaction can drive the lowest conduction Kramers’ mini bands into the quantum anomalous Hall state when they are half-filled, which is further stabilized by applying external gate voltages to break inversion. We propose the monolayer Sb2 on top of Sb2Te3 thin films as a candidate to realize our model based on the first principles calculations. Our work demonstrates the topological insulator based moiré heterostructure as a potentially appealing platform for studying interacting topological phases.