Moments are a kind of classical feature descriptors for image analysis. Orthogonal moments, due to their computation efficiency and numerical stability, have been widely developed. We propose a set of orthogonal polynomials which are derived from the parity of Hermite polynomials. The new orthogonal polynomials are composed of either odd orders or even ones of Hermite polynomials. They, however, are orthogonal in different domains. The corresponding orthogonal moments, Hermite-Fourier moments are defined. The computation strategy for these new moments is formulated in addition. Image reconstruction in comparison with Zernike moments as well as Fourier-Mellin moments shows the better image representation ability of the proposed moments.