Abstract: Controlling the convexity and strain energy of interpolating curve can be carried out by controlling the second-order derivative of the interpolating function．In literature，algorithm for rational cubic spline with linear denominator has been developed to control the convexity and strain energy of the interpolating curve，but it does not work in some cases．This paper introduces the weighted rational cubic spline with linear denominator for solving such kind of constraints，the sufficient and necessary conditions for controlling the convexity and strain energy of the interpolating curve are derived，and some examples are given．