The electronic tunneling process in a molecular device consisting of a composite symmetric multiple potential barriers in series is modeled by a simplified successive tunneling model.Patterns of the low-bias conductance of a molecule are inferred by the changing patterns of electronic transmission spectra with variations of the width

height of the barrier

the distance of the two neighboring barriers

and the efficient mass of electron.It is found that the low-bias conductance of a molecule decreases remarkably with an increase in either the width or height of a barrier

instead the low-bias conductance of a molecule increases substantially with an increase in either the distance of the two neighboring barriers or the efficient mass of electron.The results presented here suggest that the transport behaviors of molecular electronic devices under a low bias can be greatly modified in a controlled way (for example

altering the constituents or/and configurations of a composite molecule).