Aiming at the interval multi-criteria decision-making problems with uncertain criteria weights, a multi-criteria decision-making approach is proposed. Firstly, the probability of each alternative under each criterion is given through statistical inference principle, in which the whole alternative values are used as samples. Then, the value function may be offered based on the possibility degree of interval number, a non-linear programming mode with maximum degree of differentiation among all the alternatives is constructed to rank the alternatives. Finally, a numerical example illustrates the feasibility and effectiveness of the proposed method.