We have performed the 125Te-nuclear magnetic resonance (NMR) measurement in the field along the b axis on the newly discovered superconductor UTe2, which is a candidate of a spin-triplet superconductor. The nuclear spin–lattice relaxation rate divided by temperature 1=T1T abruptly decreases below a superconducting (SC) transition temperature Tc without showing a coherence peak, indicative of UTe2 being an unconventional superconductor. It was found that the temperature dependence of 1=T1T in the SC state cannot be understood by a single SC gap behavior but can be explained by a two SC gap model. The Knight shift, proportional to the spin susceptibility, decreases below Tc, but the magnitude of the decrease is much smaller than the decrease expected in the spin-singlet pairing. Rather, the small Knight-shift decrease as well as the absence of the Pauli-depairing effect can be interpreted by the spin triplet scenario.