The potential energy surface for the reaction of atomic hydrogen with propyne has been studied at the G3//UB3LYP/6-31G(d) level of theory. Three reaction entrances were revealed, namely, terminal addition, nonterminal addition, and direct H-abstraction, leading to CH3CCH2, CH3CHCH, and H-2+C3H3, respectively. The respective activation barriers are 1.7, 3.9, and 8.4 kcal/mol. The CH3-extrusion from CH3CHCH forms C2H2 via a barrier of about 32 kcal/mol. Several H-shift paths along the CCC skeleton were also examined for three C3H5 isomers. Multichannel RRKM and TST calculations have been carried out for the total and individual rate constants over a wide range of temperatures and pressures. The total rate constants possess both positive temperature dependence and typical "S" shaped fall-off behavior. At atmospheric pressure, the collisional stabilization of the initial adducts dominates the H+CH3CCH reaction at temperatures lower than 500 K, and at T > 1000 K, CH3 and C2H2 are the major products. Moreover, the direct H-abstraction channel also contributes significantly to the overall reaction. The theoretical results are compared with those of previous studies.