The problem of description wavefront aberrations in non-circle apertures was discussed. The correlation matrix of Zernike polynomials in arbitrary non-circle apertures was obtained by numerical integral. The Gram-Schmidt orthogonalizing process was done in the non-circle aperture to make a series of orthogonal polynomials based on linear combination of Zernike polynomials. Characteristics of the orthogonal polynomials in non-circle apertures are similar as the Zernike polynomials in circular apertures. Based on the orthogonal polynomials, the modal wavefront reconstruction algorithm for Hartmann-Shack wavefront sensor in non-circle apertures was also discussed.