To be environmentally friendly, reducing the energy consumption of vehicles is the trend of solving vehicle routing problems (VRPs). This paper considers the green VRP problem by using a load varying green VRP (LVGVRP) that is generally suitable for both fossil fuel vehicles and alternative fuel vehicles (AFVs), and we also study LVGVRP problems with stochastic demands (LVGVRPSD). We develop a mathematical model to formulate the LVGVRPSD optimization problem based on fact that the energy consumption rate is directly proportional to the total weight of the vehicle, and we use the risk probability to constrain the impact of stochastic customer demands. A hybrid tabu-search improved simulated annealing algorithm (HSAA) is proposed to solve the LVGVRPSD problem, in which k-means clustering, local search, and tabu-list guided searching are used to improve the results of SAA. We conduct experiments on 20 commonly used benchmarks, and the results prove that considering varying vehicle load can obtain better routes with lower energy cost. In addition, the results also prove that HSAA can achieve better objective compared with existing SAA.