Synthetic aperture radar (SAR) tomography (TomoSAR) estimates scene reflectivity along elevation coordinates, based on multi-baseline measurements. Common TomoSAR approaches are based on every single range-azimuth cell or the cell's neighborhood. By using an additional synthetic aperture for elevation, these techniques have higher resolution power for elevation, to discriminate scatterers with differences in location in the same range-azimuth cell. However, they cannot provide sufficient range resolution power to discriminate these scatterers by joining different spectra to a wider range spectrum, which limits the resolution power of TomoSAR. Therefore, in this paper, we proposed using a compressive sensing (CS) technique to reconstruct range and elevation signals from multi-baseline SAR images. This TomoSAR method not only retrieves the vertical signals but also improves the resolution in the range, which helps improve the resolution power of the TomoSAR technique. We present the theory of the CS-based two-dimensional TomoSAR technique and compare it to the CS-based one-dimensional TomoSAR technique. The excellent resolution power and scatterer localization accuracy of this novel technique are demonstrated using simulations and real data obtained by RADARSAT-2 in Lanzhou, China.