We study odd-even high-order harmonic generation (HHG) from oriented asymmetric molecules HeH2+ numerically and analytically.The variational method is used to improve the analytical description of the ground-state wave function for the asymmetric system,with which the ground-state-continuum-state transition dipole is evaluated.The comparison between the odd-even HHG spectra and the improved dipoles allows us to identify and clarify the complex generation mechanism of odd-even harmonics from asymmetric molecules,providing deep insights into the relation between the odd-even HHG and the asymmetric molecular orbital.