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Parallel storage systems have been highly scalable and widely used in support of data-intensive applications. In future systems with the nature of massive data processing and storing, hybrid storage systems opt for a solution to fulfill a variety of demands such as large storage capacity, high I/O performance and low cost. Hybrid storage systems (HSS) contain both high-end storage components (e.g. solid-state disks and hard disk drives) to guarantee performance, and low-end storage components (e.g. tapes) to reduce cost. In HSS, transferring data back and forth among solid-state disks (SSDs), hard disk drives (HDDs), and tapes plays a critical role in achieving high I/O performance. Prefetching is a promising solution to reduce the latency of data transferring in HSS. However, prefetching in the context of HSS is technically challenging due to an interesting dilemma: aggressive prefetching is required to efficiently reduce I/O latency, whereas overaggressive prefetching may waste I/O bandwidth by transferring useless data from HDDs to SSDs or from tapes to HDDs. To address this problem, we propose a multi-layer prefetching algorithm that can judiciously prefetch data from tapes to HDDs and from HDDs to SSDs. To evaluate our algorithm, we develop an analytical model and the experimental results reveal that our prefetching algorithm improves the performance in hybrid storage systems.