A method for reducing the degree of B-spline curves based on constrained least squares approximation is presented, which preserves endpoints of the B-spline curves. To make the degree reduced B-spline curve has better approximation, and its number of the control points and the knot vector are also discussed. It is presented that the method based on constrained least squares approximation, which adds a weight function to the object function for reducing the error of approximation. Furthermore, for the interval whose error is larger than the given tolerance, a method of knot insertion is presented so that the degree reduction is controlled under the tolerance. The new method is compared with the existing ones via examples.