In this paper, an approximation approach is presented for offsetting curve by approximating the normal curve of the base curve using Legendre least-square polynomials. After computing the perturbed vectors, the offset curve can be obtained by shifting the control points of the base curve. By the comparison with other approaches based on shifting control points, such as the methods by Tiller, Cobb, Coquillart and Elber, etc., it shows that the approximated offset curve obtained by this approach has the least numder of control points and the least time of subdivision for the curves.The approximated offset has the same form with the original curve.This approach is of intuition and of easy implementation.It,has imposing foreround of application.