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The concept of smart grid has emerged as a convergence of traditional power system engineering and information and communication technology. It is vital to the success of next generation of power grid, which is expected to be featuring reliable, efficient, flexible, clean, friendly, and secure characteristics. In this paper, we propose an efficient and privacy-preserving aggregation scheme, named EPPA, for smart grid communications. EPPA uses a superincreasing sequence to structure multidimensional data and encrypt the structured data by the homomorphic Paillier cryptosystem technique. For data communications from user to smart grid operation center, data aggregation is performed directly on ciphertext at local gateways without decryption, and the aggregation result of the original data can be obtained at the operation center. EPPA also adopts the batch verification technique to reduce authentication cost. Through extensive analysis, we demonstrate that EPPA resists various security threats and preserve user privacy, and has significantly less computation and communication overhead than existing competing approaches.