Abstract: The setup of the collinear fast ion-beam-laser spectroscopy (CFIBLS) with the Fabry-Prot interferometer is described and the method of analyzing the experimental data is given. The hyperfine structures of the transitions from metastable 4f95d7H08 to excited states 4f96p3/2(15/2, 3/2) for 159TbII was measured by CFIBLS. For the high spectral (sub-Doppler) resolution of CFIBLS, the HFS constants A and B of the involved levels were obtained with small errors.