The magnetic moment and electric quadrupole moment of a neutron-rich nucleus 1 8 N have been determined by the β-NMR method, taking advantage of the fragment spin polarization induced in the intermediate-energy projectile fragmentation reaction. To assure the existence of a sufficient polarization prior to the resonance search, a scheme of polarization measurement by means of an adiabatic field rotation has been developed and successfully incorporated in the β-NMR experiment. From the observed resonance in a Pt stopper the magnetic moment for the 1 8 N ground state has been determined to be μ =0.3279+/-0.0013μ N . The 1 8 N fragments have also been implanted in a single crystal Mg stopper, and from the observed quadrupole frequency eqQ/h =73.2+/-1.4 kHz, the electric quadrupole moment Q =12.3+/-1.2 mb has been deduced. The obtained μ and Q are compared with shell model calculations.