Facility location, supply inventory and distribution, and evacuation planning are key operational functions in a humanitarian relief network, it is critical to integrate these three functions and schedule their activities jointly in a coordinated manner. Considering uncertain demands and evacuation rates of injured people, we develop a distributionally robust model for the multi-period humanitarian relief network design with multiple types of relief supplies. To solve the problem, we reformulate the proposed model into a mixed integer linear programme, and develop an enhanced branch-and-Benders-cut algorithm that incorporates some algorithm enhancements to solve the resulting model. Extensive numerical experiments show that: (i) the distributionally robust model provides more reliable and flexible solutions that perform the best when faced uncertainty over the deterministic and stochastic models; (ii) the algorithm enhancements are very effective to enhance the performance of the proposed algorithm, which can reduce the CPU time by up to 9.75%∼41.64% on average; (iii) the integrated solution approach is more beneficial to solve the problem when comparing with a sequential solution approach; and (iv) some model parameters have significant impact on the solution structure, which can help decision maker set proper parameters to achieve the desired trade-off among the considered metrics.