We investigated the characteristics of molecular orientation induced by a nonresonant two-color femtosecond laser field. By analyzing the rotational dynamics of asymmetric linear molecules, we revealed that the critical parameter in characterizing the molecular orientation was the hyperpolarizability of molecules that selected the excitation paths of rotational states between parity-changing and parity-conserving transitions. Especially, in the case of molecules with small hyperpolarizability, a significant enhancement of orientation was achieved at the half-rotational period, instead of the full-rotational period. This deeper understanding of the hyperpolarizability-dependent characteristics of molecular orientation in a two-color scheme can provide an effective method to achieve significantly enhanced field-free orientation for various polar molecules.