Aming at the problem of correction algorithms of tooth profile errors of Oerlikon cycloidal bevel formate gear， by using the vector operation method， the geometric model of the tooth surface of gear is established. The method of tooth surface discretization is provided， and the coordinates and normal vectors of the discrete points on the tooth surface are calculated. Based on the principle of tooth profile error correction， the tooth profile error correction equation group is established based on the tooth profile error and inverse parameter sensitivity coefficient matrix between the actual tooth surface and the theoretical tooth surface. By using the Tikhonov regularization and L curve optimization algorithm， the linear equation group is solved， the correction value of the adjustment parameter of the machine tool is obtained. The software for tooth surface coordinate calculation and tooth profile error correction is developed by using Fortran. The correctness of the correction algorithm is verified by experiments and the maximum tooth profile error of the experimental workpiece is reduced from 37.5 μm to 5.2 μm.