In this paper, we first construct a time consistent multi-period worst-case risk measure, which measures the dynamic investment risk period-wise from a distributionally robust perspective. Under the usually adopted uncertainty set, we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure. Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.