Time-dependent hybrid density functional theory in combination with polarized continuum model is applied to study the solvent effects on the geometrical and electronic structures as well as one- and two-photon absorption processes,of a newly synthesized asymmetrical charge-transfer organic molecule bis-(4-bromo-phenyl)-[4-(2-pyridin-4-yl-vinyl)phenyl]-amine (BPYPA). There exist two charge-transfer states for the compound in visible region. The two-photon absorption cross section calculated by a three-state model and solvatochromic shift of the charge-transfer states are found to be solvent-dependent, where a nonmonotonic behaviour with respect to the polarity of the solvents is observed. The numerical results show that the organic molecule exhibits a rather large two-photon absorption cross section as compared with the compound 4-trans-[p-(N, N-Di-n-butylamino)-p-stilbenyl vinyl] pyridine (DBASVP) reported previously, and is predicted to be a good two-photon polymerization initiator. The hydrogen-bond effect is analysed. The computational results are in good agreement with the measurements.