The nondegenerate nu-2 <-- 0 and 2-nu-2 <-- nu-2 bands of the ammonia cation NH3+ have been observed using tunable diode lasers combined with the velocity modulation technique. The ion was produced in a water-cooled 6 kHz ac glow discharge cell with a gas mixture of [He]:[N2]:[H2] = 9:0.06:0.3 (Torr). From the observed spectra, the band origins were determined to be nu-1 <-- 0 = 903.3893 cm-1 and nu-2 <--1 = 939.771 cm-1. Vibration-rotation interaction constants and potential constants were derived. The missing of K = 0 R-branch transitions with N = odd in the nu-2 <-- 0 band and N = even in the 2-nu-2 <-- nu-2 band clearly shows the characteristics of a D3h planar structure with a 2A2" ground electronic state, just like its isoelectronic case CH3 radical. Spin-rotation doublets were well-resolved in R-branch transitions and spin-rotation interaction constants of the ground, nu-2, and 2-nu-2 states were determined. A potential function consisting of a quadratic term and a quartic term was used for modeling the out-of-plane bending vibration of NH3+. In comparison with the methyl radical, the ammonia cation is more rigid and closer to a harmonic oscillator.