The multi-valued neutrosophic set, the multi-valued neutrosophic number and its expected value as well as the Hamming distance between two multi-valued neutrosophic numbers are defined. Besides, the comparison rules between two multi-valued neutrosophic numbers are also given. For the multi-criteria decision making with multi-valued neutrosophic sets, the traditional TODIM method is extended, and an approach is given. In this method, a reference criterion is selected and then a value function is built based on the Hamming distance between multi-valued neutrosophic numbers. This value function is used to get the ranking order of all alternatives. Finally, a numerical example is given to show the effectiveness and feasibility of the proposed method.