Low earth orbit (LEO) satellite internet of things (IoT) is a promising way achieving global Internet of Everything, and thus has been widely recognized as an important component of sixth-generation (6G) wireless networks. Yet, due to high-speed movement of the LEO satellite, it is challenging to acquire timely channel state information (CSI) and design effective multibeam precoding for various IoT applications. To this end, this paper provides a deep learning (DL)-based joint channel prediction and multibeam precoding scheme under adverse environments, e.g., high Doppler shift, long propagation delay, and low satellite payload. {Specifically, this paper first designs a DL-based channel prediction scheme by using convolutional neural networks (CNN) and long short term memory (LSTM), which predicts the CSI of current time slot according to that of previous time slots. With the predicted CSI, this paper designs a DL-based robust multibeam precoding scheme by using a channel augmentation method based on variational auto-encoder (VAE).} Finally, extensive simulation results confirm the effectiveness and robustness of the proposed scheme in LEO satellite IoT.