Aiming at a type of vehicle routing problems with multiple time windows under fuzzy demand (VRPMTW_FD) that exists widely in reality, which is that the customer demand is fuzzy before the vehicle is delivered but the customer demand becomes definite after the vehicle reaches the customer, a fuzzy chance constrained programming model based on the fuzzy credibility theory is constructed to minimize the total cost, and a two-stage hybrid optimization algorithm (TSHOA) is proposed to solve it. Firstly, the first stage of the TSHOA designs an improved gray wolf optimizer (IGWO) to solve the VRPMTW with fuzzy customer demand before vehicle delivery, to obtain the pre-optimized path of the VRPMTW_FD. Then, in the second stage of the TSHOA, the optimal point rescheduling strategy (OPRS) is designed to dynamically adjust the pre-optimized path, so as to determine the appropriate return point to reduce the additional distribution cost due to the failure of the pre-optimized path. Through simulation experiments and algorithm comparisons on different scale problems, it is verified that the TSHOA can effectively solve the VRPMTW_FD.