In-storage computing with modern solid-state drives (SSDs) enables developers to offload programs from the host to the SSD. It has been proven to be an effective approach to alleviating the I/O bottleneck. To facilitate in-storage computing, many frameworks have been proposed. However, few of them consider security as the priority for in-storage computing. Specifically, since modern SSD controllers do not have a trusted execution environment, an offloaded (malicious) program could steal, modify, and even destroy the data stored in the SSD. In this paper, we first investigate the attacks that could be conducted by offloaded in-storage programs. To defend against these attacks, we build IceClave, a lightweight trusted execution environment for in-storage computing. IceClave enables security isolation between in-storage programs and flash management functions. IceClave also achieves security isolation between in-storage programs and enforces memory encryption and integrity verification of in-storage DRAM with low overhead. To protect data loaded from flash chips, IceClave develops a lightweight data encryption/decryption mechanism in flash controllers. We develop IceClave with a full system simulator and evaluate IceClave with a variety of data-intensive applications. Compared to state-of-the-art in-storage computing approaches, IceClave introduces only 7.6% performance overhead, while enforcing security isolation in the SSD controller with minimal hardware cost. IceClave still keeps the performance benefit of in-storage computing by delivering up to 2.31$\times$ better performance than the conventional host-based trusted computing approach.