A class of cubic parameter curve of B-spline type is constructed in this paper with four arbitrary parameters, the cubic Hermite curve, Ball curve, Bezier curve, Timmer curve and B-spline curve as its special cases. The condition in which the curves contact with each edge of characteristic polygon is also given. In order to satisfy the actual riquirements,the shape(i. e. location of end point,direction of convixity and flexion,etc. )of curves can be modified by adjusting the four parameters.