In this paper, we deal with the vehicle routing problem where vehicles have finite capacities and demands of customers are uncertain. We represent the uncertain demands by fuzziness and interpret them as possibility distributions. According to the same consideration as the fuzzy programming with recourse, we treat the influence of the fuzzy of customers' demands as recourse cost. Defining the fuzzy number as it's the generalized mean value, the proposed model is equivalent to an ordinary programming problem and then a solution method based on Particle Swarm Optimization (PSO) can be proposed to give the best solution of the problem. Finally, some examples are given to illustrate the two-stage model and the solution algorithm.