Quadratic hyperbolic polynomial basis functions with multiple shape parameters are presented in this paper， which possess the most properties of quadratic non-uniform B-spline basis functions. Based on the basis functions， quadratic hyperbolic polynomial curves with multiple shape parameters are constructed. These curves are C1-continuous with a non-uniform knot vector .With different values of the shape parameters，the shapes of the curves can be adjusted totally or locally .Without using multiple knots or solving equations，the curves can be interpolated given certain control points or control polygon edges directly. And hyperbolic polynomial curves can represent hyperbolas exactly.