We construct a continuum model for the moiré superlattice of twisted bilayer MnBi_{2}Te_{4}, 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 MnBi_{2}Te_{4}.