Jacobi-Fourier moments (JFM),which choose Jacobi polynomial as radial function and Fourier factor as angle function are proposed. The new moments are generalized Orthogonal Fourier-Mellin moments. Jacobi-Fourier moments can be normalized to be invariant for shifting,scaling,rotation and intensity distortion of an image. The normalized image reconstruction error (NIRE) and noise sensitivity of Jacobi-Fourier moments are also investigated. Results show that Jacobi-Fourier moments are good image feathers with strong image description ability andn noise resistange power. Compared with other researches, the research view is extended from reconstructing a certain function to reconstructing a function family.