In real-world environments, vehicle travel and service time will be affected by unpredictable factors and present a random state. Because of this situation, this paper proposes the vehicle routing problem with soft time windows and stochastic travel and service time (SVRP-STW). The probability distribution of vehicle travel and service time are introduced into the model, and a stochastic programming model with modification is established to minimize the distribution cost. An Improved Tabu Search algorithm (I-TS) based on greedy algorithm is proposed, in which adaptive tabu length and neighborhood structure are introduced; the greedy algorithm is used instead of the random methods to generate the initial solution. Experiments on different scale instances prove the effectiveness and superiority of the proposed algorithm. INDEX TERMS Stochastic travel times, stochastic service times, soft time windows, stochastic programming model, tabu search.