The In-doped topological crystalline insulator Sn1-xInxTe is a promising candidate for a topological superconductor, where it is theoretically suggested that In creates an impurity state responsible for superconductivity. We synthesized high purity Sn1-xInxTe samples and performed Te-125-nuclear magnetic resonance (NMR) measurements. The NMR spectra under a magnetic field of H-0 = 5T show a broadening characteristic due to a localized impurity state. The spin-lattice relaxation rate (1/T-1) divided by temperature shows a Curie-Weiss like temperature-dependence under H-0 = 0.1 T but is temperature-independent under H-0 = 5T. These results indicate the existence of quasi-localized impurity states due to In doping.