The travel times among demand points are strongly influenced by traffic in a supply chain. Due to this fact, the service times for customers are variable. For this reason, service time is often changes over a time interval in a real environment. In this paper, a time-dependent periodic green vehicle routing problem (VRP) considering the time windows for serving the customers and multiple trip is developed with this assumption that urban traffic would disrupt timely services. The objective function of proposed problem is to minimize the total amount of carbon dioxide emissions produced by the vehicle, earliness and lateness penalties costs and costs of used vehicles. At first, a novel linear integer mathematical model is formulated and then the model is validated via solving some test problems by CPLEX solver. Finally, the sensitivity analysis is carried out to study the role of two critical parameters in the optimal solution.