  We report the $^{207}$Pb nuclear magnetic resonance (NMR) measurements on
polycrystalline sample of PbTaSe$_2$ with noncentrosymmetric crystal structure
and topological electronic band. The nuclear spin-lattice relaxation rate
$1/T_1$ shows a suppressed coherence peak below the superconducting transition
temperature $T_{\rm c}$ = 4.05 K and decreases as an exponential function of
temperature. The penetration depth derived from the NMR spectrum is almost
temperature independent below $T$ = 0.7 $T_{\rm c}$. The Knight shift $K$
decreases below $T_{\rm c}$. These results suggest spin-singlet
superconductivity with a fully-opened gap $2\Delta = 3.5$ $k_{\rm B}T_{\rm c}$
in PbTaSe$_2$.
