Single-crystalline Sb2Te3 nanostructures, of which the bulk is one of the best thermoelectric materials at room temperature, are synthesized by chemical vapor deposition. The composition, crystal structure, and growth mechanism of the sample are investigated. According to our experimental results, Sb2Te3 normally grows into hexagonal nanoplates without using catalyst, but single-crystalline nanowires can be fabricated with Au nanoparticles as the catalyst. The growth mechanism of Sb2Te3 nanostructures is closely related to its anisotropic crystal structure. Sb2Te3 has a rhombohedral structure, which exhibits a layered anisotropy with the Te and Sb atom layers arranged along the c-axis. Moreover, there are two adjacent Te layers connected by van der Waals bonds. Therefore, Sb2Te3 prefers to grow into hexagonal plates in the ab-plane. When Au nanoparticles are used as the catalyst, the growth direction of the precipitated Sb2Te3 is restricted, leading to the formation of Sb2Te3 nanowires.