To overcome the shortcomings of the traditional interpolation spline that is difficult to add or delete points and the inaccuracy of the traditional approximate spline, we propose an approximate algorithm based on the cubic B-spline. The algorithm, which is based on the approximation and the iteration, improves the calculation speed and precision. Based on the periodic cubic B-spline curves, the algorithm extends to quartic B-spline, which is third derivative. Besides, the theoretical proof of the convergence of the algorithm is given out. Finally, the numerical approximation experiments on common functions show that the algorithm has a faster convergence speed and can meet higher practical industrial needs.