A new model of k( k ≥ 3) order exponential polynomial uniform spline is given.Most of its properties similar to those of the B - spline model, and also it has an adjustable shape parameter. The spline curves which are constructed by the exponential polynomial uniform splines can adjust the curve's shape and degrees between the curve and its control polygon by changing the parameter value. The new model can be applied to the field of CAD/CAM.