A complex optical model potential modified by incorporating the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule, is firstly employed to calculate the total cross sections for positron scattering from CO, HCl, NH3, SiH4 in the incident energy range 30—3000eV by using additivity rule model at Hartree-Fock level. In the study, the complex optical model potential composed of static, correlation polarization plus absorption contributions firstly uses the bonded-atom concept. The results of quantitative molecular total cross sections are compared with those obtained by experiments and other theories wherever available, and good agreement is obtained. It is shown that the additivity rule model together with the complex optical potential model modified by incorporating the concept of bonded atom can give much better calculation results than the unmodified one.