The leakage of privacy is one of the key factors to restrict the development of smart grid. Currently, research works of protecting privacy in smart grid mainly focused on two aspects: (1) data aggregation based on the mathematical model and algorithm and (2) user anonymous authentication. However, data aggregation is at cost of obtaining fine-grained electricity consumption information to protect privacy. Anonymous authentication cannot identify the malicious user in previous studies. Hence, in this work, we propose a group blind signature scheme in smart grid to accomplish conditional anonymity. Furthermore, the integrity of consumption data can be verified by homomorphic encryption (HE) which can decrease the communication overhead between control center and smart meter remarkably. From the security analysis and experiment simulation, the results show that our scheme is safe and efficient.