Magnetic properties in the quasi-one-dimensional organic salt, (TMTTF)(2)SbF6, where TMTTF is tetramethyltetrathiafulvalene, are investigated by C-13 NMR under pressures. Antiferromagnetic phase transition at ambient pressure (AFI) is confirmed. Charge ordering is suppressed by pressure and is not observed under 8 kbar. For 5 < P < 20 kbar, a sharp spectrum and the rapid decrease of the spin-lattice relaxation rate 1/T-1 were observed below about 4 K, which is attributed to a spin-gap transition. Above 20 kbar, an extremely broadened spectrum and a critical increase of 1/T-1 were observed. This indicates that the system enters into another antiferromagnetic phase (AFII) under pressure. The slope of the antiferromagnetic phase transition temperature T-AFII, dT(AFII)/dP, is positive, while TAFI decreases with pressure. The magnetic moment is weakly incommensurate with the lattice at 30 kbar.