We have studied the one-photon absorption （OPA） and two-photon absorption （TPA） properties of the one-, two- and three-dimensional compounds with the same unit of （4-{2-［4-（2-pyridin-4-yl-vinyl）-phenyl］-vinyl}-phenyl）-amine moieties, using the response theory approach at the hybrid density functional theory level. The numerical simulation shows that the three organic molecules exhibit strong OPA and TPA capabilities. All chromophores present two linear absorption peaks in the ultra UV-visible region, which is in agreement with the experimental measurements. Strong broadband TPA properties from 780 to 1020 nm have been demonstrated in the near infrared region. The ratio of the largest TPA cross sections for three molecules DPVPA, BPVPA and TPVPA is 1.0∶2.3∶4.0, and the molecule TPVPA has the maximum TPA cross section 101.73×10-48 cm4·s. It is substantiated that the TPA cross section can be effectively enhanced with increasing molecular dimensionality. The charge-transfer process for the charge-transfer state is visualized in order to understand the enhancement of the TPA cross sections.