This paper proposes to use the trust region dogleg method to solve the high nonlinearity problem of post finishing of general aspheric optical components. Firstly, based on the low-order body representation and the homogeneous transformation method, a forward kinematic model suitable for any aspherical surface shape and arbitrary path is established. Then, a strong nonlinear forward kinematic model is established based on the trust region dogleg method. The numerical optimization method is used to obtain the corresponding inverse kinematics numerical results. Finally, the inverse kinematics numerical solution results are processed to obtain the control values of each axis for post processing. For an off-axis aspheric surface with an initial surface shape of root mean square 0.037λ, after four rounds of finishing with a raster line path planning and five rounds of finishing with a spiral path planning, the surface shape of the processed component converges to root mean square 0.012λ, and the total convergence efficiency reaches 67.57%, indicating that the proposed post-processing method is correct and can be used for aspheric processing.