According to the uncertainty of the customers in city logistics, a stochastic programming model with recourse is formulated to solve the split delivery vehicle routing problem(VRP) with stochastic customers. Based on the priori optimization strategy, an adaptive large neighborhood search heuristic with modified split insertion operator is developed. Computation tests on the modified Solomon's instances are carried out. The results show that, in most of the instances, the cost of split delivery is lower than unsplit-delivery. In the computation, the deterministic worst removal operator and the random removal operator are the best removal operators, and the greedy insertion and the regret insertion are the best insertion operator. Though the weight of the split insertion operator is lower, it makes the solution different from the unsplit-delivery solution.