The research proposes arbitrary shaped aperture wavefront fitting (ASAWF) for arbitrary shaped aperture wavefront fitting and aberration removing. It departs from the traditional Zernike polynomials only ideal for wavefront reconstruction of circular wavefronts but not non-circular wavefronts. The approach preserves the orthogonality of the Zernike polynomials in arbitrary shaped aperture wavefronts and addresses the coefficient coupling problems of the non-circular shaped aperture wavefront fitting known adversely affecting aberration removal. The ASAWF method is used to fit non-circular regions with an orthogonal matrix using the modified Gram–Schmidt orthogonalization technique with QR decomposition and point cloud. The ASAWF method is employed to fit the arbitrary shaped aperture wavefront, including elliptical, square, and irregular shape wavefronts. The proposed method is confirmed through numerical simulation and experimental data demonstrating the effectiveness of wavefront reconstruction and aberration removal.