Clock network synthesis is one of the most important and challenging problems in 3-D ICs. The clock signals have to be delivered by through-silicon vias (TSVs) to different tiers with minimum skew. While there are a few related works in literature, none consider the reliability of TSVs in a clock tree. Accordingly, the failure of any TSV in the clock tree yields a bad chip. The naive solution using double-TSV can alleviate the problem, but the significant area overhead renders it less practical for large designs. In this paper, we propose a novel TSV fault-tolerant unit (TFU) to provide tolerance against TSV failures. The TFU makes use of the existing 2-D redundant trees designed for prebond testing, and thus has minimum area overhead. In addition, the number of TSVs in a TFU is also adjustable to allow flexibility during clock network synthesis. Compared with the conventional double TSV technique, the 3-D clock network constructed by TFUs can achieve 58% area overhead reduction with similar yield rate on an industrial case. To the best of the authors' knowledge, this is the first work in the literature that considers the fault tolerance of a 3-D clock network. It can be easily integrated with any bottom-up clock network synthesis algorithm.