One-photon and two-photon absorption properties of a double-conjugated-segment molecule (BSBAB) composed of two single-conjugated-segment molecules are studied by using density functional theory at ab initio level. The optimized geometrical structure shows that the two single-conjugated-segment parts in molecule BSBAB retain their own coplanarity and are nearly perpendicular to each other, which seems to indicate that the molecule BSBAB contains optical characteristics of both parts. The molecule BSBAB is found to have three two-photon absorption peaks in lowest energy region which are contributed respectively the two single-conjugated-segment parts respectively and the coupling between them. This also demonstrates that the molecule BSBAB is a broadband strong two-photon absorption chromophore. The response theory approach at Hatree-Fock level is used to prove the convergence of results given by the state summation method with truncated approximation. The charge-transfer process between the charge-transfer states is visualized. The theoretical results are in good agreement with the measurements.