A crucial issue in humanitarian relief operations is vehicle routing because there are many difficulties in roads that people face when a disaster is occurred. In such circumstances, selecting more reliable routes could help rescue team act more efficacious. Therefore, we propose a mathematical model that maximizes the reliability of selected routes in disaster relief routing process using a multiple attribute decision making (MADM) technique. Furthermore, the proposed model minimizes the total cost that imposed to system. For this reason, the model is a multi-objective vehicle routing problem (VRP). The problem considered here is NP-hard and its objective is to find near optimal solutions, rather than optimal ones, using the non-dominated sorting genetic algorithm.