In 5G mobile communication systems, the beamforming technology is used with massive antenna elements to improve the received power and spectral efficiency within a cell. To improve the throughput of the entire system, it is also necessary to improve the spectral efficiency at the cell boundary where the communication quality tends to deteriorate because of inter-cell interference. Multi-cell coordinated beamforming is effective for mitigating the inter-cell interference and improving the cell boundary performance; antenna beamforming is jointly controlled among multiple base stations to avoid the inter-cell interference at the cell boundary. In this paper, we propose a coordination method for antenna beamforming among multiple base stations; this method improves the communication quality at the cell boundary without deteriorating the communication quality of the entire cell. For the propagation model of the computer simulation, we have considered urban areas with buildings around the terminals. In comparison with the conventional individual beamforming, our proposed method improved upon the communication quality by approximately 4 dB at the cell boundary without any deterioration of the whole cell.