At a Li density of -1013 cm-3,the lithium vapor was irradiated in a five-arm stainless steel heat pipe oven containing Li and H2 with pulses of radiation from a N2-laser-pumped dye laser,populating Li(2P) state by the Li(２S→2P) resonance transition at 670.8 nm. Typical operating pressure of H2 was 60-300 Pa. The cross section for Li(2P)+H2→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 H2 against its densities yielded a slope that indicated the total cross section for deactivation and an intercept (at which the H2 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 H2 is (25.1±4.0)×10-16 cm2. 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 H2 densities. The authors fitted a two-state rate equation model to obtain the cross section σ(Li(2P)+H2→LiH+H)=(0.2±0.1)×10-16 cm2. 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.