Near infrared spectrum of the 3v(2), overtone band (v(2)=3<--0) of H-3(+) has been observed at 1.4 mu m. The spectrum is weaker than the v, fundamental band by a factor of similar to 250. High sensitivity plasma spectroscopy using velocity modulation and unidirectional multiple passing has enabled us to observe 15 rovibrational transitions. Short-external-cavity InGaAsP diodes were used as tunable near infrared radiation sources. The narrow tuning range and the availability of diodes limited the observation to a fraction of observable transitions. Nevertheless, the observed results provide information on the rovibrational energy of the 3v(2)(l=1) state which may be used to further improve the variational calculations by Miller and Tennyson.