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Due to the strong analytical ability of big data, deep learning has been widely applied to train the collected data in industrial IoT. However, for privacy issues, traditional data-gathering centralized learning is not applicable to industrial scenarios sensitive to training sets. Recently, federated learning has received widespread attention, since it trains a model by only relying on gradient aggregation without accessing training sets. But existing researches reveal that the shared gradient still retains the sensitive information of the training set. Even worse, a malicious aggregation server may return forged aggregated gradients. In this paper, we propose the VFL, verifiable federated learning with privacy-preserving for big data in industrial IoT. Specifically, we use Lagrange interpolation to elaborately set interpolation points for verifying the correctness of the aggregated gradients. Compared with existing schemes, the verification overhead of VFL remains constant regardless of the number of participants. Moreover, we employ the blinding technology to protect the privacy of the gradients submitted by the participants. If no more than n-2 of n participants collude with the aggregation server, VFL could guarantee the encrypted gradients of other participants not being inverted. Experimental evaluations corroborate the practical performance of the presented VFL framework with high accuracy and efficiency.