This paper presents a two-layer time window assignment vehicle routing problem (TL-TWAVRP(. It is assumed that there is a predefined time window determined by the customers which is called exogenous time window. Also, there are two-layer endogenous time windows inside the previous one. The outer layer has bigger width and the difference is a violation variable. These new time windows give a flexibility to career companies for visiting customers after the end of assigned time windows to perform services to more customers. If the vehicle arrives at the customer in her/his inner layer assigned time window, no penalty is paid but if vehicle violates inner layer, a penalty will be calculated in the objective function. No extra violation is allowed from the outer layer assigned time window. This problem is modeled as a two-stage stochastic problem. The first-stage decisions are assigning inner and outer layers time window to each customer. In the second stage, routes will be planned for each scenario. Finally, by comparing this model with the TWAVRP, it has been shown that the proposed model has better performance to minimize total cost with serving more customers considering their exogenous time windows.