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Exploring spin-orbit coupling (SOC) in single-layer materials is important for potential spintronics applications. Using first-principles calculations, we show that single-layer antimony telluroiodide SbTeI behaves as a two-dimensional semiconductor exhibiting a band gap of 1.82 eV. More importantly, we observe the Rashba spin splitting in the SOC band structure of single-layer SbTeI with a sizable Rashba coupling parameter of 1.39 , which is significantly larger than that of a number of two-dimensional systems including surfaces and interfaces. The low formation energy and real phonon modes of single-layer SbTeI imply that it is stable. Our study suggests that single-layer SbTeI is a candidate single-layer material for applications in spintronics devices.