Constrained data interpolation is important in many sciences and engineering based disciplines. For instance, the robot path problem always can be considered as constrained data interpolation. Thus, this study the constrained data interpolation using C2 rational cubic spline with three parameters. The data dependent sufficient condition is derived on one parameter meanwhile the other two parameters can be used to modify the interpolating curve. The unknown first derivatives are calculated by solving tri-diagonal systems of linear equations through Thomas's algorithm. From all numerical results, it can be concluded that the proposed scheme research very well and on par with some established schemes. © Medwell Journals, 2018.