The magneto-transport properties of (111)-oriented single-crystal thin films of SnTe were investigated. SnTe (111) thin films were epitaxially grown on a BaF₂ substrate by molecular beam epitaxy. By optimizing the growth conditions and the thickness of the films, the bulk carrier density could be reduced, making it possible to detect the surface transport. Magneto-conductance (MC) measurements show a cusp-like feature around zero magnetic field, which is attributed to the weak-antilocalization effect of the transport in the topological surface state. Detailed analysis of this negative MC reveals a reduced number of transport channels contributing to the surface transport, suggesting strong coupling between Dirac valleys on the SnTe (111) surface, as a characteristic feature of the transport in the multivalley structure of topological crystalline insulators.