Abstract: To improve the performance of Zernike moment, this paper focuses on the fractional order Zernike moment, which is a generalization of the traditional integer order one. An algorithm is proposed to construct these fractional order Zernike moments. Firstly, the radial part of traditional Zernike polynomial is transformed to replace the integer order polynomial of the traditional Zernike moment by the fractional order polynomial, which makes the traditional Zernike only a special case of the construction. Then, the orthogonality and rotation invariance of the proposed fractional order Zernike moment are proved. At last, experimental results show that fractional order Zernike moments with better performance for noise and reconstruction can be constructed by the proposed method.