Surface interpolation plays an important role in many applications of science and engineering. Usually the collected data are obtained from any observations or experimentation. These raw data need to be visualized by using some mathematical techniques to produce smooth curves or surfaces that resembles the original data sets. In this chapter, a new surface interpolation based on rational bi-quartic spline is constructed. Partially blended rational bi-quartic spline is employed on all four rectangular curves network. There are 12 free parameters for shape modification and refinement. From numerical results, the proposed scheme is highly accurate since the root mean square error (RMSE) is small and the resulting interpolating surface is smooth compared with some existing schemes. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.