One of the most important and yet complex decision-making problems in the area of transportation programming issues is vehicle routing problem. There are various exact, heuristic, and metaheuristic methods presented for solving different vehicle routing problems. In this manuscript, a mathematical model and a new heuristic solution method are proposed for solving multi-depot vehicle routing problem with time windows and different types of vehicles. In this problem, depots must serve customers between their fuzzy time windows with vehicles having different capacities, velocities, and costs. For this purpose, the mathematical model for multi-depot routing problem is developed to consider the mentioned circumstances. The objectives of this model is travel distance reduction and customers' service level increscent which leads to cost and service time reduction. For complexity of this problem and much computational time of exact solutions of developed model, a heuristic approach is proposed. This systematic approach has some steps as: customer clustering, routing, vehicle type determination, scheduling, and routes improvement using simulated annealing and customer service level improvement. The efficiency of the proposed method is analyzed by a case study in ISACO Co. Results show that the method is efficient and applicable in industries.