Abstract: The h-Bézier curves are a family of generalized Bézier curve, by adding positive real weights, the obtained rational h-Bézier curve can represent conic sections accurately. In order to obtain conic sections with monotonic curvature, a constructive method for monotonic curvature quadratic rational h-Bézier curves is proposed for standard type quadratic rational h-Bézier curves. Firstly, introducing the curvature extremum circles, the existence of the curvature extremum of the standard form quadratic rational h-Bézier curve is discussed. Secondly, using the curvature monotonic critical circles, a necessary and sufficient condition for the curvature monotonicity of standard type quadratic rational h-Bézier curves are obtained, for given initial and final control vertices, in order to obtain a conic section with monotonic curvature, just insure the intermediate control vertex on or within the curvature monotonic critical circle. Furthermore, based on the necessary and sufficient conditions for curvature monotonicity, location of the intermediate control vertex, the weight factor w, and the shape parameter h are properly selected to construct a curvature monotonic quad ratic rational h-Bézier curve. Numerical examples are constructed to obtain quadratic rational h-Bézier curves with monotonically decreasing or increasing curvature. Compared with the conditions for monotonic curvature of quadratic h-Bézier curves and quadratic rational Bézier curves, proposed method provides wider ranges of parameter h and intermediate control vertices, making the curve modeling more flexible.