We construct a continuum model for the Moiré superlattice of twisted bilayer MnBi2Te4, and study the band structure of the bilayer in both ferromagnetic (FM) and antiferromagnetic (AFM) phases. We find the system exhibits highly tunable Chern bands with Chern number up to 3. We show that a twist angle of 1 • turns the highest valence band into a flat band with Chern number ±1 that is isolated from all other bands in both FM and AFM phases. This result provides a promising platform for realizing time-reversal breaking correlated topological phases, such as fractional Chern insulator and p + ip topological superconductor. In addition, our calculation indicates that the twisted stacking facilitates the emergence of quantum anomalous Hall effect in MnBi2Te4.Topology has become one of the central topics in condensed matter physics. The discovery of topological insulator (TI) [1][2][3][4][5][6][7][8][9][10][11], quantum anomalous Hall (QAH) effect [12][13][14][15][16][17][18] and other topological states have significantly enriched the variety of quantum matter, and may lead to potential applications in electronics and quantum computation [19][20][21][22][23]. Electron-electron interaction plays an essential role in fractional quantum Hall effect, and there have been proposals of strongly correlated topological states such as fractional TI and fractional Chern insulator (FCI) without magnetic field [24][25][26][27][28][29][30][31]. Experimentally realizing such states is, however, challenging because flat topological electronic bands are generally required for electron-electron interactions to manifest.Recently, it is shown that Moiré superlattices in twisted or lattice mismatched two-dimensional (2D) materials can give rise to flat topological bands. A prime example is twisted bilayer graphene (tBLG) [32][33][34][35], where the lowest two bands carry a fragile topology [36][37][38][39][40] and become flat near the magic twist angle θ ≈ 1.1 • . In addition, flat valley Chern bands can be realized in tBLG with aligned hBN substrate [41][42][43], twisted double bilayer graphene [44][45][46], ABC trilayer graphene on hBN [47][48][49] and twisted bilayer transition metal dichalcogenides [50,51], etc. The small bandwidths make electron-electron interactions important [52][53][54][55][56][57][58][59], and further lead to intriguing interacting phases in experiments including superconductivity, correlated insulator and QAH effect.So far, all of the experimental Moiré systems are timereversal (TR) invariant at the single particle level, thus the total Chern number always equals to zero. Therefore, even with flat bands, it is difficult to achieve TR breaking interacting topological states such as the FCI in these systems. This motivates us to consider the Moiré superlattice of TR breaking layered materials. A promising system is 3D antiferromagnetic (AFM) topological axion insulator MnBi 2 Te 4 [60-77], which can be driven into a ferromagnetic (FM) Weyl semimetal or 3D QAH insulator. The material consists of Van der Waals coupl...