As wireless sensor networks are becoming increasingly reliant on communication among heterogeneous wireless sensor nodes , the need for secure communication in multi-groups has grown tremendously. Secure group key management in the multi-group scenario is a major challenge. The existing group key management schemes focus on managing a single group. However, there is not much work done regarding secure communication in multiple groups simultaneously. Existing multi-group key management schemes usually fail to meet the performance demands and suffer from improper management of keys, violation of security requirements, or huge complexity. We have analyzed the existing schemes for secure multi-group key management and found that the major issue lies in the complexity overhead during the membership update process in the multi-group scenario. On that account, we have proposed a new and efficient scheme (BP-MGKM) for secure multi-group key management based on bivariate polynomial . BP-MGKM is more efficient than other existing schemes in the context of complexity incurred during re-keying procedures. BP-MGKM features forward and backward secrecy, resilience against node compromise attack, collusion attack, and replay attack. The proposed scheme is secure and efficient than the existing schemes.