Accurate measurement and control of wavefront aberrations in space-based telescopes are key to achieving efficient space gravitational wave detection. This paper presents a method for measuring wavefront aberrations of space-based telescopes based on the Shack-Hartmann wavefront sensor. This method employs a cross-correlation algorithm in the frequency domain after frequency domain threshold denoising. The measurement accuracy of the algorithm is verified using a Shack-Hartmann wavefront sensor with 20×16 sub-apertures, microlens dimensions of 0.279 mm×0.279 mm, and a focal length of 34 mm. Point source images with known defocus RMS values (0, 0.22, 0.44, and 0.66 nm) are generated, producing point source images with displacements. After wavefront reconstruction using the modal method, the RMS values of the reconstructed and residual wavefronts are calculated, comparing the measurement accuracy of the cross-correlation algorithm in the frequency domain with the traditional centroid algorithm. The results show that as the actual defocus value increases, the measurement error of the centroid algorithm presents an upward trend, respectively at 0.0966 nm, 0.1378 nm, 0.1284 nm, and 0.1463 nm. The cross-correlation algorithm in the frequency domain can increase the measurement accuracy by 13%, 7%, 18%, and 14% respectively, providing an important reference for the high-precision testing of wavefront aberrations of space gravitational wave space-based telescopes on the ground.