  We have performed the $^{125}$Te-nuclear magnetic resonance (NMR) measurement
in the field along the $b$ axis on the newly discovered superconductor UTe$_2$,
which is a candidate of a spin-triplet superconductor. The nuclear spin-lattice
relaxation rate divided by temperature $1/T_1T$ abruptly decreases below a
superconducting (SC) transition temperature $T_c$ without showing a coherence
peak, indicative of UTe$_2$ being an unconventional superconductor. It was
found that the temperature dependence of $1/T_1T$ 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 $T_c$, 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.
