The method and mechanism on the perfluorinated carboxylic acids (PFCAs) degradation is a hot issue. The crystal lattice structures of the anatase TiO₂(101), (001), (110), (210), the rutile TiO₂(110), (001), (101), (210) and the brookite TiO₂ (210), (101), (001), (110) were optimized with the CASTEP program in Materials Studio package based the density functional theory (DFT). It is found that the energies of the anatase (101), rutile (110) and brookite (210) are the lowest, and the most stable adsorption surfaces, respectively. The adsorption energies of the 18 kinds of the optimized modes on the most stable TiO₂ surfaces adsorbed by trifluoroacetic acid (TFA) were calculated. It is indicated that the absorption energy of the mode which the TFA is perpendicular to the brookite (210) surface and the carboxyl group of H adsorbed by Ti atom on the brookite (210) is the biggest, and the adsorption structure is the most stable, and the adsorption mode is the best. The partial state densities for the three kinds of the most stable absorption modes were calculated. It is revealed that the covalent interaction of the TFA on bookite (210) surface is weak, resulted from the narrowing of the band gap that the 2p orbital of O, F of TFA inserts into between the valence band (VB) and conduction band for TiO₂. In the best adsorption mode, before and after adsorption the band gap goes down from 3.06 eV to 2.80 eV, i.e., photocatalytic wavelength increases from 385 nm to 443 nm, so that the visible light absorption efficiency is increased.