The energy storage converter is the core carrier of the energy storage system to smooth the power fluctuations of renewable energy generation and to support the regulation of frequency and voltage. The key operation control technology of energy storage converter, especially the control strategy under current-control mode, is investigated. The tracking control strategy without static error of current inner loop is proposed. The design method of the PI control key parameters based on optimal damping ratio is proposed. Based on open-loop amplitude-phase frequency characteristic and open-loop logarithmic frequency characteristic method, the open-loop frequency domain model of the current inner loop of the energy storage converter is constructed. Through the Bode stability criterion, the influence of different current inner loop proportional coefficient, integral coefficient and converter resistance parameter change on the control stability of the energy storage converter is quantitatively analysed. At meanwhile, the Nyquist stability criterion is used to verify the results. The grid-connected test of the energy storage converter is carried out on the real time labratory (RT-LAB) platform. The grid-connected system remains stable under the different proportional coefficient and integral coefficient. Based on the transfer function of filter capacitor input voltage to output current, the problem of harmonic resonance is found. The active damping resonant suppression strategy based on capacitor current feedback is proposed, which can effectively eliminate the effect of harmonic resonance. The analysis results indicate that the proposed current-control type energy storage converter and its harmonic resonance suppression method is robustness for supporting development of renewable energy generation.