The two-photon absorption properties of two newly synthesized compounds containing fluorene as a π centre (denoted SK-G1 and NT-G1) were calculated using a response function method with density functional theory. Results show that both compounds have large one-photon and two-photon absorption abilities. In the low energy region, the maximum one-photon absorption strength of NT-G1 is twice as much as that of SK-G1 and its maximum absorption is red shifted compared to that for SK-G1. The maximum two-photon absorption cross section of NT-G1 is about five times as large as that of SK-G1 and those are found for the second excited states. Furthermore, NT-G1 has a wider two-photon absorption energy band. The optical properties of the molecules are closely related to their charge transfer processes when they are excited. The solvent effect on their one-photon absorption properties was calculated using the Onsager model. The numerical calculation is found to be in od agreement with experimental measurements.