Abstract: Compared with uniform α-B spline it is very necessary to introduce non-uniform α-B spline and investigate the possibility as well as the algorithm for the monotonicity-preserving interpolation to this kind of curve.In this paper,a family of non-uniform α-B spline interpolation curve with the shape control parameter αis constructed expediently by using singular blending function but dispensing with solving any system of equations or going at any iterative computation；then,the positive conditions of Bernstein polynomial can be used to obtain a range in which the shape parameter takes its value so as to make the corresponding interpolating curves monotonicity-preserving and C²（or G¹） continuity maintained.Several numerical examples are given to illustrate the correctness and the validity of theoretical reasoning.