Image orthogonal moments have the advantages of numerical stability an d convenient reconstruction,and Jacobi-Fourier moment (JFM) is a promotion of traditional or thogonal moment.However, its definition of the radial function is only integer order polynomial.In this paper,we transform the radial function of JFM and propose a generic Jacobi-Fourier moment.The definition of the radial function can not only be fractional order polynomial,but also can be a more general function, and JFM is just a special case of this kind of structure.Mea nwhile,we prove the orthogonality and rotation invariance of proposed generic JFM.Numerical experime ntal results also show that image orthogonal moments which are more robustness to noise and better reconstruction can be structured using the proposed method.