At a Li density of similar to 10(13) cm(-3), the lithium vapor was irradiated in a five-arm stainless steel heat pipe oven containing Li and H-2 with pulses of radiation from a N-2-laser-pumped dye laser, populating Li(2P) state by the Li(2S -> 2P) resonance transition at 670. 8 nm. Typical operating pressure of H-2 was 60-300 Pa. The cross section for Li(2P) + H-2 -> LiH + H reaction was measured using method of atomic fluorescence. The decay signal of the time-resolved fluorescence from the 2P -> 2S transition was monitored. The decay curve of the Li(2P) can be treated as a single exponential function. The effective lifetimes of the 2P state was obtained. According to the Stern-Volmer equation, a plot of reciprocal of effective lifetimes of the 2P state quenched by H-2 against its densities yielded a slope that indicated the total cross section for deactivation and an intercept (at which the H-2 pressure is zero) that provided the information about the radiative lifetime of the state. The total quenching (reactive+nonreactive) cross section for deactivation of the 2P state by means of collisions with H-2 is (25. 1 +/- 4. 0) x 10(-16) cm(2). The reactive cross section could be obtained using results of the recording of the fluorescence signals with rapid rise in transient regime (<10 ns) Li(2P -> 2S)at the different H-2 densities. The authors fitted a two-state rate equation model to obtain the cross section sigma(Li(2P) + H-2 -> LiH + H)=(0. 2 +/- 0. 1) x 10(-16) cm(2). The authors' results imply that reactive collisions occur on average 1/125 as often as quenching collisions. The cross section for reaction is small but not negligible.