The vehicle routing problem (VRP) is one of the well known optimization problems. It is used to minimize the total length of all routes of vehicles where each of the vehicle has a capacity constraint respectively. This paper proposes a self-organization neural network model for obtaining the best solution for VRP. Our method consists of two phases. In the first phase, the customers are grouped to several delivery areas for vehicles assignment by Maximum Neuron model. In the second phase, the TSP in each area is solved by Elastic net model proposed by Andrew et. al. The clustering algorithm used in the first phase is a Maximum Neuron model. Maximum Neuron model is one of the neural networks proposed by Hopfield that can minimize a cost function considering various constraints. In the second phase, Elastic net model is used to solve the problem and it can obtain good solutions of TSP. Our method improves the precision of solution, and can be extended for big size problem. Our simulation result shows that Maximum Neuron model can achieve better solutions than other methods in certain conditions.