A metaheuristic algorithm, called Harmony Search (HS) is implemented for data fitting by rational cubic Be´ zier curves. HS is a derivative-free real parameter optimization algorithm, and draws an inspiration from the musical improvisation process of searching for a perfect state of harmony. HS is suitable for multivariate non-linear optimization problem. It is mainly achieved by data fitting using rational cubic Be´ zier curves with G1 continuity for every joint of segments of the whole data sets. This approach has significant contributions in making the technique automated. HS is used to optimize positions of middle points and values of the shape parameters. Test outline images and comparative experimental analysis are presented to show effectiveness and robustness of the proposed method. Statistical testing between HS and two other different metaheuristic algorithms is used in the analysis on several outline images. All of the algorithms improvised a near optimal solution but the result that is obtained by the HS is better than the results of the other two algorithms.