Multiple resonances may result in instability of a LCL filter based multiple grid connected converter (MGCC) system. This paper investigates the critical factors of multiple resonances in MGCC system. It is found that, closed-loop output admittance of the grid connected converter can be configured to meet the requirements of resonances suppression, by properly designing control method and parameters. To improve the multiple resonances suppression, a control method is applied to the MGCC system, which is a combination of proportional resonant (PR) control and full state feedback control. According to the proposed design principle of the closed-loop output admittance, a case study using the control method above is given. Simulation results are provided to validate the correctness and effectiveness of the proposed design principle and control method.