We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C=1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C=3 and an $N$-band square lattice model with $C=N$ for an arbitrary integer $N$. In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate inter-particle interactions, these models are likely to lead to the formation of novel Abelian and Non-Abelian fractional Chern insulators. As a simple example, we test the C=2 model with hardcore bosons at 1/3 filling and an intriguing fractional quantum Hall state is observed.