In order to reduce the distribution cost of fresh food logistics and achieve the goal of green distribution at the same time, the Green Fresh Food Logistics with Heterogeneous Fleet Vehicle Route Problem (GFLHF-VRP) model is established. Based on the particularity of the model, an improved genetic algorithm called Genetic Algorithm with Adaptive Simulated Annealing Mutation (GAASAM) is proposed in which the mutation operation is upgraded to a simulated annealing mutation operation and its parameters are adjusted by the adaptive operation. The experimental results show that the proposed GAASAM can effectively solve the vehicle routing problem of the proposed model, achieve better performance than the genetic algorithm, and avoid falling into a local optimal trap. The distribution routes obtained by GAASAM are with lower total distribution cost, and achieve the goal of green distribution in which energy, fuel consumption and carbon emissions are reduced at the same time. On the other hand, the proposed GFLHF-VRP and GAASAM can provide a reliable distribution route plan for fresh food logistics enterprises with multiple types of distribution vehicles in real life, which can further reduce the distribution cost and achieve a greener and more environment-friendly distribution solution. The results of this study also provide a managerial method for fresh food logistics enterprises to effectively arrange the distribution work with more social responsibility.