During the past few years, there have tremendous efforts on improving the cost of logistics using varieties of Vehicle Routing Problem (VRP) models. In fact, the recent rise on fuel prices has motivated many to reduce the cost of transportation associated with their business through an improved implementation of VRP systems. We study a specific form of VRP where demand is supposed to be uncertain with unknown distribution. A Particle Swarm Optimization (PSO) is proposed to solve the VRP and the results are compared with other existing methods. The proposed approach is also used for real world case study of drug distribution and the preliminary results indicate that the method could reduce the unmet demand significantly.