We propose a method for detecting multiple scatterers (targets) in the elevation direction for synthetic aperture radar tomography. The proposed method can resolve closely spaced targets through a two-step procedure. In the first step, coarse detection is performed with a successive cancellation scheme in which possible locations of targets are marked. Then, in the second step, by searching in the reduced search space, which is finely gridded, the accurate location of the targets is found. For estimating the actual number of targets, a model order selection scheme is used in two cases of known and unknown noise variance. Also, by analytical investigation of the probability of detection for the proposed method, the effect of the influential parameters on the detection ability is explicitly demonstrated. Compared to the super-resolution methods based on compressed sensing, the proposed method has a lower computational cost and higher estimation accuracy, especially at low signal-to-noise ratio regime. Simulation results show the superiority of the proposed method in terms of both three-dimensional scatterer reconstruction and detection ability.