Nowadays, transportation and logistics are considered as the drivers of economic development in the countries due to their impacts on the main variables of the country's economy such as production, employment, price, and the cost of living. Statistics indicate that fuel consumption constructs a major part of transportation costs, where its optimization leads to the creation of an energy-efficient and sustainable transportation system. On the other hand, vehicles' traffic is also one of the main criteria affecting the travel time of vehicles between demand nodes in a supply chain, increasing fuel consumption, and, consequently, damaging effects of greenhouse gasses. In this paper, a novel robust mixed-integer linear programming model is developed for a green vehicle routing problem with intermediate depots considering different urban traffic conditions, fuel consumption, time windows of services, and uncertain demand for perishable products. To validate and solve the suggested model, CPLEX solver of GAMS software is employed as an exact method. Finally, a case study problem is investigated to evaluate the applicability of the proposed model and determine the optimal managerial insights and policies in the real-world conditions using sensitivity analyses. Moreover, a novel robustness threshold comparison is conducted to find the optimal level of budget assignment.