Abstract: Fourier descriptor is an important method used in shape analysis and recognition. In this paper, an efficient and accurate method is used to calculate Fourier descriptors of the shape by polygonal approximation, and a method of removing the phase effect of the start point of the border through a shape’s main orientation is presented. A new normalized Fourier descriptor is defined, which is invariant in the rotation, translation and scale transform. The experiments show the accuracy and efficiency of the new normalized Fourier descriptors in shape recognition.