A set of moments was proposed based on Bessel function under three kinds of boundary conditions, named Bessel-Fourier moments, which are defined in polar coordinate and regarded as a generalized orthogonality complex moment. The radical polynomials of the Bessel-Fourier moments have many zero points and most of them are distributed uniformly. The reconstruction experiments of 26 uppercase binary images and the classification experiments of 1260 gray butterfly images were used to validate the proposed method, and different Bessel-Fourier moments under three kinds of boundary conditions wre extracted as the feature values of image analysis (image descriptor). Theoretical and experimental results show that, compared with the orthogonal Fourier-Mellin and Zernike moments, the Bessel-Fourier moments are more suitable in image analysis and rotation-invariant object recognition, and performed better than the orthogonal Fourier-Mellin and Zernike moments in terms of image reconstruction capability and invariant recognition accuracy.