This paper focuses on the affection of the curved surface media. In order to study it, the continuous wave penetrating radar (CWPR) is applied to detect targets buried in the spherical media. The antennae move in a plane above the spherical surface and execute two dimensions sampling. Different from planar media, this special geometry makes the echoes of the surface interfere, and several circular interference fringes which awfully degrade the imaging quality could be found. In this paper, a novel method is proposed to remove the interference fringes for improving the spherical subsurface imaging. Due to the geometric symmetry, a distribution difference in spatial spectrum domain between the echo of spherical surface and back-scattering field of target beneath the surface can be found out subsequently when a 2D Fourier transformation has been conducted on the data matrix. Therefore, a filter based on this difference is designed to remove the disturbance of interference fringes. Taking advantage of spatial spectrum filtering, CWPR successfully wipes off the fringes caused by spherical surfaces and makes substantial progress in image quality of the subsurface imaging. Moreover, the numerical simulation and experiment results validate the availability of the proposed method.