A new octupolar compound 2,4,6-tris{4[4-(dibutylamino)phenylethynyllphenyl]-1,3,5-triazine was synthesized and characterized. The first hyperpolarizability beta of it has been investigated by Hyper-Rayleigh scattering (HRS) measurements. A facile data processing method was proposed to eliminate the influence of the relatively weak three-photo-absorption induced fluorescence (3PF) irradiated by laser beam at lambda = 1500 nm. The values of beta(1500) and beta(0)(1500) are close to those obtained at lambda = 1600 nm laser beam at which no multi-photon-absorption induced fluorescence is detected, validating this method. This method is useful for the investigation of the first hyperpolarizability beta with weak absorption induced fluorescence.