We present a new method to estimate the wavefront with the curvature-sensing technique proposed by F. Roddier. Instead of solving a Poisson equation for the curvature signal, we estimate the wavefront by direct least-squares curve fitting of the curvature signal with derivatives of Zernike polynomials. It is computationally simpler and faster. From computer simulations, it is shown that the curve-fitting method gives quite accurate wavefront estimation. It is especially useful when only a fixed number of aberration modes are of interest, as in the optical-axis adjustment of a telescope.