With the rapid development of energy Internet (EI), energy storage (ES), which is the key technology of EI, has attracted widespread attention. EI is composed of multiple energy networks that provide energy support for each other, so it has a great demand for diverse energy storages (ESs). All of this may result in energy redundancy throughout the whole EI system. Hence, coordinating ESs among various energy networks is of great importance. First of all, we put forward the necessity and principles of energy storage coordination (ESC) in EI. Then, the ESC model is constructed with the aim of economic efficiency (EE) and energy utilization efficiency (EUE) respectively. Finally, a multi-agent particle swarm optimization (MAPSO) algorithm is proposed to solve this problem. The calculation results are compared with that of PSO, and results show that MAPSO has good convergence and computational accuracy. In addition, the simulation results prove that EE plays the most important role when coordinating various ESs in EI, and an ES configuration with the multi-objective optimization of EE and EUE is concluded at last.