Analysis and utilization of massive meter data can help decision-makers provide reasonable decisions. Therefore, multi-functional meter data processing has received considerable attention in recent years. Nevertheless, it might compromise users' privacy, such as releasing users' lifestyles and habits. In this paper, we propose an efficient and privacy-preserving massive data process for smart grids. The presented protocol utilizes the Paillier homomorphic encryption and Horner's Rule to achieve a privacy-preserving two-level random permutation method, making large-scale meter data permuted randomly and sufficiently in a privacy-preserving way. As a result, the analysis center can simultaneously implement various data processing functions (such as variance, comparing, linear regression analysis), and it does not know the source of data. The security analysis shows that our protocol can realize data confidentiality and data source anonymity. The detailed analyses demonstrate that our protocol is efficient in terms of computational and communication costs. Furthermore, it can support fault tolerance of entity failures and has flexible system scalability.