In fringe projection profilometry, carrier removal is required to obtain the absolute height information of the tested object. We propose using radial basis function interpolation methods, due to their good approximation properties, to accurately remove the carrier phase. We evaluate the proposed method on a simulated fringe projection pattern with a nonlinear carrier and two experimentally obtained fringe projection patterns, respectively. The performance of the proposed method is compared to those of the widely used least-squares method and recent Zernike polynomial fitting method. Experimental results show that the proposed method has an improved performance.