For adaptive optics with curvature sensor, two close-loop wavefront control techniques those based on direct fitting method and Laplacian eigenfunctions method are comparative analyzed. The basic principles of two methods are analyzed, and then a numerical simulation model of 36-element curvature adaptive optics is setup and simulations of atmospheric turbulence wavefront aberration correction are carried out. The results show that, comparing with the direct fitting method, the stability and correction accuracy of Laplacian eigenfunctions method are obvious better when the proper modes are chosen, and the stability and accuracy of the direct fitting method are significantly worse when the phase distortion is larger.