The aim of this paper is to establish some inequalities for bounding the gamma function that yields sharp asymptotic estimates for as tends to . Our results improve several known results stated by Alzer [H. Alzer, Inequalities for the gamma function, Proc. Amer. Math. Soc., 128 (1) (1999) 141–147], Andreson and Qiu [G.D. Anderson, S.-L. Qiu, A monotonicity property of the gamma function, Proc. Amer. Math. Soc., 125 (1997), 3355–3362], and Li and Chen [J. Choi, Some mathematical constants, Appl. Math. Comput., 187 (2007) 122–140].