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Mobile edge computing (MEC) is an emerging technology to transform the cloud-based computing services into the edge-based ones. Autonomous vehicular network (AVNET), as one of the most promising applications of MEC, can feature edge learning and communication techniques, improving the safety for autonomous vehicles (AVs). This paper focuses on the edge learning in AVNET, where AVs at the edge of the network share model parameters instead of data in a distributed manner, and an aggregator (e.g., a base station) aggregates parameters from AVs and at the end obtains a trained model. Despite promising, security issues, such as data leakage, computing integrity invasion and fault connection in existing edge learning cases are not considered fully. To the best of our knowledge, there lacks an effective scheme simultaneously covering the foregoing security issues. Therefore, we propose \textit{SecEL}, a privacy-preserving, verifiable and fault-tolerant scheme for edge learning in AVNET. First, we leverage the primitive of bivariate polynomial-based secret sharing to encrypt model parameters by one-time padding. Second, we use homomorphic authenticator based on message authentication code to support verifiable computation. Third, we mitigate the computation failure problem caused by fault connection. Last, we simulate and evaluate SecEL in terms of time cost, throughput and classification accuracy. The experiment results demonstrate the effectiveness of SecEL.