This paper discussed the local control of interpolating function by using rational cubic spline (cubic/quadratic) with three parameters originally proposed by the authors. The rational spline has C 1 continuity. The bounded properties of the rational cubic interpolants and shape controls of the rational interpolants are discussed in detail. The value control, inflection point control, and convexity control at a point by using the proposed rational cubic spline are constructed. Several numerical results are presented to show the capability of the method. Numerical comparisons with the existing scheme are also further elaborated. From the results, it was indicated that the scheme works well and it is comparable with the established existing scheme. © 2014 Samsul Ariffin Abdul Karim and Kong Voon Pang.