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As a new meta-heuristic, bat algorithm has not yet been applied to solve fuzzy vehicle routing problem until now. In this paper, the vehicle routing problem with fuzzy demands is considered at first, in which the final objective is to minimize the total distance, and then a fuzzy programming model based on fuzzy credibility theory is presented, in order to solve this problem, an improved bat algorithm with the coding method of customer number is introduced. In this algorithm, a stochastic simulation is proposed to calculate the additional distance, moreover, a nonlinear adjustment strategy for the inertia weight and a local search strategy on sub-route are designed at the stage of location updating of each bat, on the other hand, to improve the global search ability of this algorithm and avoid premature convergence, crossover operation on the worst bats is applied. To illustrate the effectiveness and good performance of the proposed algorithm, an example is carried out by using the random experimental data, and the influence of the decision-maker’s preference on the objective of this problem is discussed, moreover, the improved bat algorithm is compared with other algorithms.