Privacy-preserving data aggregation is an important technology for mobile crowdsensing. Blockchain-assisted data aggregation enables the traceability of sensing data to improve the trustworthiness of data aggregation results. However, directly using blockchains for data aggregation may introduce the risk of privacy leakage because all nodes, including malicious nodes, can access the data on blockchains. In this paper, we propose a grouping-based reliable privacy-preserving data aggregation (RPPDA) method using private blockchains for mobile crowdsensing. First, the sensing nodes are divided into multiple groups, and each group maintains a private blockchain to store the data aggregation records, which avoids the leakage of the aggregated results and ensures the traceability of the sensory data. Then, a zero-sum noise-adding mechanism is utilized to not only preserve the private information during aggregation and ensure the correctness of the aggregated results but also improve the efficiency of privacy preservation. Furthermore, we theoretically prove the correctness, privacy, efficiency, and reliability of the proposed RPPDA algorithm. Real-world and simulated experiments demonstrate the effectiveness and advantages of the proposed RPPDA algorithm in terms of correctness, efficiency, and privacy.