In sensor networks, a group key plays an important role in both secure group communication and some security services such as false date filtering. Considering the security threat that there may be plenty of compromised nodes, a new group key management scheme based on random perturbation and secret sharing techniques is proposed (GKRP for short). In the GKRP, base station and local networks manage group keys cooperatively; additionally, some functions such as the broadcast rekeying function and local collaboration function are constructed. Thus, with GKRP, even if there are plenty of compromised nodes, these nodes can be revoked in real-time to ensure group key security. Extensive analyses and simulations show that GKRP can provide a higher level of security because GKRP is not limited to the compromised nodes under certain conditions, which can be satisfied easily. Moreover, GKRP is also more efficient on communication as taking local broadcast and network broadcast to rekey. The storage and computation overheads of GKRP are somewhat higher than some related works; however, they are still lightweight and thus are suitable to sensor networks.