In this paper, we propose EPIC, an efficient and privacy-preserving data collection scheme with EtoE data integrity verification for advanced metering infrastructure networks. Using efficient cryptographic operations, each meter should send a masked reading to the utility such that all the masks are canceled after aggregating all meters' masked readings, and thus the utility can only obtain an aggregated reading to preserve consumers' privacy. The utility can verify the aggregated reading integrity without accessing the individual readings to preserve privacy. It can also identify the attackers and compute electricity bills efficiently by using the fine-grained readings without violating privacy. Furthermore, EPIC can resist collusion attacks in which the utility colludes with a relay node to extract the meters' readings. A formal proof and probabilistic analysis are used to evaluate the security of EPIC, and ns-3 is used to implement EPIC and evaluate the network performance. In addition, we compare EPIC to existing data collection schemes in terms of overhead and security/privacy features.