With the massive deployment of the Internet of Things (IoT) devices, many data analysis applications emerge for the large amount of data accumulated by IoT. Federated learning (FedL) on IoT devices is an appealing mode to train a precise data analysis model. However, existing FedL schemes either take expensive computation costs (e.g., public-key cryptographic operations) or a large number of interactions among participants. Obviously, these schemes are unsuitable for IoT devices due to the limited computational and communication resources. In this work, we propose a lightweight privacy-preserving FedL scheme for IoT devices. To protect the privacy of individual local data, we add masks to intervening parameters. An effective secret-sharing scheme is adopted to ensure that masks can be eliminated accurately. Considering that FedL involves multiple iterations and mask generation for each iteration costs a large number of interactions among users for privacy guarantee, we also design a secure mask reusing mechanism for large-scale FedL tasks. We prove that our scheme is secure against the honest-but-curious model. In addition, we also expand our scheme to deal with the collusion attack. Extensive experiments on real IoT devices demonstrate the accuracy and efficiency of our work.