The robust optimization models for multi-period inventory based on the max-min method are developed under the uncertain discrete demand probability. The interval and ellipsoid uncertain sets which the uncertain demand distribution belongs to are considered, and the multi-period inventory robust optimization models are transformed to tractable convex programmings by using the dual theory. The numerical results show that, comparing to the optimal condition with full distribution information, the robust ordering strategies will lead to performance loss, but the loss is very small. The results show that the multi-period inventory strategies derived by robust optimization has superior robustness, so that can reduce the impact of demand distributional uncertainty on the multi-period inventory operation performance.