Based on the classical numerical reconstruction method, the reconstructed image according to different depth section of the three-dimensional object would be disturbed by the twin image and out-of-focus section image. Therefore, a numerical reconstruction method according to compressive sensing theory for a single off-axis Fresnel hologram is proposed to achieve tomographic imaging. First, the adaptive filtering method is applied to the hologram to eliminate the twin image. And then, based on the compressive sensing theory, different depth section images can be reconstructed with the background out-of-focus object inhibited. The numerical simulation and digital holography experiment employing test targets are performed to demonstrate the feasibility and validity of the method.