We have designed a series of trans-stilbene derivatives with different arrangement of the substituents and studied their one-photon and two-photon absorption properties by using the response theory methods at HF level. The calculations show that these molecules have strong two-photon absorption cross sections. In the visible light region, the maximum two-photon absorption cross section for molecules with asymmentric substitution of the donor and acceptor occurs in the first excited state, while for the symmetric substitution cases it occurs in the fourth excited state. The asymmetry-substituted molecules have a larger two-photon absorption cross section than the symmetry substituted molecules, indicating that the effect of the different kinds of substituents on the two-photon absorption of molecules is related to the property of theiry π-centers. The charge-transfer process for the charge-transfer states was visualized in order to understand their maximal two-photon absorption cross sections.