  We have performed $^{139}$La,$^{31}$P-NMR studies on a filled skutterudite
superconductor LaFe$_{4}$P$_{12}$ with a critical temperature $T_c=4.1$ K. In
the normal state, the presence of antiferromagnetic (AFM) fluctuations at
finite wave vectors is suggested from the relation between the nuclear
spin-lattice relaxation rate $1/T_1$ and the Knight shift. In the
superconducting (SC) state, the distinct coherence peak was observed just below
$T_c$, and is easily suppressed by the applied field. An exponential decrease
of $1/T_1$ was observed, suggestive of the isotropic superconducting gap with
$2\Delta/k_{\rm B}T_c =3.8$. Besides, we observed the decrease of the Knight
shift, indicative of the singlet-pair formation below $T_c$. These results are
clear evidence that LaFe$_{4}$P$_{12}$ is a rare s-wave superconductor with
significant AFM fluctuations.
