Aiming at the problems of vehicle imbalance and charging optimization of shared autonomous electric vehicle (SAEV) operation, an optimal control strategy based on cloud-edge coordination calculation for SAEV was proposed. Firstly, a SAEV rebalancing optimization model and a rebalancing task allocation algorithm were proposed. Secondly, considering V2G and dynamic electricity price to optimize the charging and discharging of SAEV fleet, a SAEV fleet energy exchange model and a trip order allocation algorithm were proposed to reduce the charging cost of the entire SAEV fleet system. Then, the cloud-edge coordination communication was used to transfer these optimization results among different platforms, so as to realize the optimal charging and moving strategy of electric vehicles. Finally, the optimization control method was verified in MATLAB by using the real Shenzhen taxi data. The results show the framework can reduce the charging costs and improve the transportation efficiency, and is expected to be applied to larger scale of systems. The proposed cloud-edge coordinative control strategy divides the complex SAEV optimization problem into three sub-problems, and provides a new method and idea for the optimal operation of SAEV.