The cubic spline interpolation is frequently used for analysis the data set in various aspects of engineering and science problem. For a large set of data points defined with very large range, it is very difficult to interpolate by using traditional sequential algorithm. In this paper, we proposed a more systematic approach which has a parallel component known as skeleton which is implemented in various parallel paradigms like OpenMP, MPI, and CUDA etc. It is interesting that the skeleton approach is used with pipelining technique that gives better result as compared to the previous studies. This approach is applied to compute the cubic spline interpolating polynomial based on a large data set. The experimental result using the parallel skeleton technique on multi-core CPU and GPU shows better performance with respect to other parallel methods.