Concerning the problem of high energy consumption existing in Cloud storage Content Distribution Network (CCDN), the energy consumption optimization method for the CCDN was studied. Firstly, the operation principle of CCDN was analysed. Then, the energy consumption formulas were given for each cloud server and each network link. Moreover, the weighted graph was used to describe the whole network. Furthermore, based on the weighted graph, an energy consumption optimization algorithm named Min-Energy-Graph (MEG) was designed to satisfy the Quality of Service (QoS) of CCDN and data distribution of network system. MEG was compared with Greedy Site (GS) and Optimal Static Placement and Routing (OSPR) by the simulation experiments. Compared with the GS and OSPR, the energy consumption of MEG was reduced by 6.6% and 30% respectively in the experiment of system extension, the energy consumption of MEG was reduced by 28.9% and 60.2% separately in the experiment of ensuring the user QoS, and the energy consumption of MEG was reduced by 32.2% and 89.3% independently in the experiment of network topology density. The experimental results show that the proposed energy management method can greatly reduce the energy consumption of CCDN.