In a typical smart grid, a large number of smart meters are deployed at energy consumers' premises, which can report real-time usage data to the control center of the energy producer. Although such a communication model can help to improve the efficiency and reliability of electricity delivery, which is crucial to our society, it also leads to several security issues: (1) attackers may violate the privacy of energy consumers, and (2) attackers may tamper with the transmitted data for their own benefits or purposes. To deal with these security issues, many researchers have proposed different schemes for privacy preservation or abnormal data detection. However, existing studies usually address them separately. In this paper, we jointly resolve these two major security issues in the smart grid. Specifically, we propose a privacy-aware data dissemination scheme for smart grid with abnormal data traceability (PDDS), based on bilinear group theory and non-interactive zero-knowledge proof. In our scheme, we design a novel link function that can verify whether there are different signatures that are signed by the same consumer, which effectively reduces the time and communication overhead for tracing. To evaluate the correctness and performance of the proposed scheme, we first develop a solid security analysis, which shows that the proposed scheme can efficiently preserve identity confidentiality and data integrity. We then conduct extensive simulation experiments, which further demonstrate that our scheme can significantly reduce communication costs. (C) 2016 Elsevier B.V. All rights reserved.