Abstract: Based on the fairing requirements of the strain energy and jerk energy of a thin elastic beam，a method of fairing C-B spline curves is given.The mean idea is：Fairing of C-B spline curves is fulfilled by adjusting the value of parameterand control points to reduce the implied energy.By using the technique of least square approximation and non-linear functional minimization，the data points of plane can be faired approximately.Finally，examples of C-B spline curve fairing show the efficiency of the method.The numerical example shows that this algorithm provides an effect and new method for the fairing of C-B spline curves.