One of the most important factors in a humanitarian supply chain during a disaster is to respond quickly and efficiently. Delivering emergency commodities to the affected areas is critical in reducing consequences. Moreover, transferring the injured people through the fastest and the shortest time by using all available resources is vitally important. To this aim, a multi-echelon, multi-objective forward and backward relief network is proposed that considers the location of hospitals, local warehouses and hybrid centers, which are hospitalwarehouse centers in the pre-disaster phase. In the post-disaster phase, the routing of relief commodities is considered in the forward route. In the backward route some vehicles that can transfer injured people after delivering commodities; hybrid transportation facilities; will take injured to hospitals and hybrid centers. According to the degree of hardness, a hybrid nondominated sorting genetic algorithm (NSGA-II) with simulated annealing (SA) and variable neighborhood search (VNS) algorithms is proposed to solve the given problems. The results of this hybrid algorithm are compared with NSGA-II and multi-objective SA-VNS using five metrics (i.e., a number of Pareto, mean ideal distance, spacing, diversity and time) to emphasize that the proposed hybrid algorithm outperforms the two foregoing algorithms.