The basic vehicle routing problem model usually needs to be extended in order to solve real-world vehicle routing problems. Time dependent vehicle routing problem is a vehicle routing problem in which travel costs along the network are dependent upon the time of day during which travel is to be carried out. Most of the models for vehicle routing reported in the literature assume constant and deterministic travel times, This paper describes a route construction method for time dependent vehicle routing problem with fuzzy traveling times according to different traffic conditions. Our designed heuristic algorithm is based on nearest neighborhood which has two constraints as capacity and time restrictions. During selection of the new node, these constraints have been taken into consideration.