The first measurement of a magnetic moment of N-19 was performed by combining a beta-NMR method with a spin-polarized radioactive nuclear beam from the fragmentation reaction. As a result, the g value for the N-19 ground state, g = 0.61 +/- 0.03(preliminary), was obtained. The value was compared with those of N-15 and N-17. Contrary to shell-mode predictions that the g value should increase with increasing number of neutrons in the sd shell, the obtained g for N-19(g.s.). is significantly smaller than g(N-17(g.s.)) previously obtained.