Recently, asymmetric molecules, such as HeH\(_2^+\), CO, OCS, HCl, have been evolved much attention since its rich information in the high-order harmonic generation (HHG), whose ratio of adjacent even and odd harmonics characterizes the asymmetry of molecules. In this paper, we study the dependence of even-to-odd ratio on the asymmetric parameters, in particular, the nuclear-charge ratio, and the permanent dipole, by exploiting a simple but general model of asymmetric molecules \(Z_1Z_2\) subjected to an intense laser pulse. The HHG is simulated by the numerical method of solving the time-dependent Schrödinger equation. We find out that this even-to-odd ratio strongly depends on the nuclear-charge ratio. In particular, the even-to-odd ratio reaches its maximum when the nuclear-charge ratio is about from 0.5 to 0.7. Besides, the dependence on the permanent dipole of the even-to-odd ratio has a non-trivial law. To explain, we calculate the analytical ratio of the transition dipole according to the emission of even and odd harmonics, and this ratio is well consistent with the even-to-odd ratio of the HHG.