We study high-order harmonic generation (HHG) from multi-center asymmetric linear molecules numerically and analytically. Our simulations show that odd and even HHG spectra of the asymmetric multi-center system respond differently to the change of the molecular structure. Specifically, when the internuclear distances between these nuclei of the molecule have a small change, the odd spectra usually do not change basically, but the even spectra differ remarkably. Based on this phenomenon, a simple procedure is proposed to probe the positions of these nuclei with odd-even HHG. Our results shed light on attosecond probing of the structure of multi-center molecules using HHG.