The recent IEEE 802.16j-2009 adds multi-hop relay capabilities to IEEE 802.16 systems, which aims to offer improved coverage and capacity over single-hop radio access systems. In this paper, we point out several security issues, including non-authenticated privacy and key management messages, insecure relay multicast rekeying algorithm and insecure Multicast and Broadcast Rekeying Algorithm (MBRA), of the key management protocols in IEEE 802.16j-2009 and give some solutions. In particular, we propose a new Secure MBRA (SMBRA) based on identity and logical key tree to solve the security issues of MBRA. SMBRA can not only provide backward and forward secrecy of communications but also avoid key forgery. Furthermore, our theoretical analysis and simulation indicate that SMBRA is much more efficient and adequate, especially in a large group.