A simple and an efficient algorithm for polygon morphing is proposed in this paper. We adopt the parametric curve representation based on Fourier parameter estimation to transfer the traditional morphing process in spatial domain to a process in the parametric space instead. The principles are to express the polygon as the union of matching segments that are described by the estimated Fourier parameters. We have also designed a data resampling method that effectively controls the shape morphing according to the corresponding curvature values. Intermediate objects in-between the source and target polygons are then constructed based on the interpolation of Fourier parameters of the two polygons. Fourier parameters of the resampled polygons can be obtained efficiently by using the fast Fourier transform (FFT) algorithm. The experimental results show that the appearances of the morphed objects are superior to the ones obtained by the methods available.