Abstract: To make multi-points tangent contact machining have higher computational efficiency, an improved algorithm based on Hermite method was proposed. Theoretical analyses were given on the convergence of the improved algorithm, and the constraints for local convergence of the new algorithm were also derived. Then the formula of steffensen accelerated iterative method was applied on the algorithm. Another novel algorithm called iterative method of undetermined coefficient based on trial method was developed. The results show that the improved algorithm based on Hermite method acts as a linear convergence method, while the iterative method of undetermined coefficient algorithm has the same convergence speed with square convergence method approximately. Then it can meet the demand for the tool path generating computation of general sculpture surface by combining all the above-mentioned algorithms applied on them.