The shape of cubic B-spline curve is fixed to its control polygon.In addition,it cannot describe the conic section besides the parabola.In order to overcome disadvantages,a set of algebraic-trigonometric blending spline basis,which enjoys many nice properties,was constructed. A kind of new curve,which structure was similar to the classical cubic B-spline curve,was defined.The new curve not only inherited the major advantages of the cubic B-spline curve,but also enjoyed shape adjustability,and it exactly expressed circle,ellipse, parabola,sine curve,cosine curve,cycloid and cylinder helix.For equidistant knots,the new curve was C2continuous,and it achieved C3 continuity when taking special shape parameter.In addition,how to choose control points to make the new curve tangent to a given control polygon was discussed.