Traort a substantial part of each nation's gross domestic product allocated to one of the largest consumers of oil products considered. In recent years, many efforts have been made to reduce greenhouse gas emissions by vehicles. As the use of petroleum products caused by greenhouse gas emissions, reducing the use of these products can make a major contribution to reducing pollution. Traort is one of the main elements of the logistic and inventory routing problem one of the most important issues in this field. In this problem, distribution and inventory management decisions taken together. Today, usually by the use of several different properties and assess the composition of the fleet, while reducing inventory costs and routing decisions may be appropriate. In this thesis provided A Novel Bi-Objective Model for Fleet Size and Mix Green Inventory Routing Problem. The proposed model aims to minimize the emissions and minimizing, fleet composition, routing and inventory costs. This model offers a choice of puts it in the hands of decision-makers, and will be flexible in making decisions. Also can be used in different circumstances that may be out of control is effective. According to NP-hard presented model, Quantum multi-objective Evolutionary Algorithm is proposed. In order to investigate the proposed algorithm results with the results of the exact solution (Epsilon Constraint) and Non Dominated Sorting Genetic Algorithm are compared. The results showed performance of the proposed algorithm is better .