Coordinated multi-point (CoMP) joint transmission is considered in the 3rd generation partnership project (3GPP) long term evolution (LTE)-advanced as a key technique to mitigate inter-cell interference and improve the cell-edge performance. To effectively apply CoMP joint transmission, efficient frequency reuse schemes need to be designed to support resource management cooperation among coordinated cells. However, most of the existing frequency reuse schemes are not suitable for CoMP systems due to not considering multi-point joint transmission scenarios in their frequency reuse rules. In addition, the restrictions of frequency resources in those schemes result in a high blocking probability. To solve the above two problems, a multi-beam cooperative frequency reuse (MBCFR) scheme is proposed in this paper, which reuses all the available frequency resources in each sector and supports multi-beam joint transmission for cell-edge users. Besides, the blocking probability is proved to be efficiently reduced. Moreover, a frequency-segment-sequence based MBCFR scheme is introduced to further reduce the inter-cell interference. System level simulations demonstrate that the proposed scheme results in higher cell-edge average throughput and cell-average throughput with lower blocking probability.