For non-sidelooking airborne radar operating in medium pulse repetition frequency mode, the space-time adaptive processing (STAP) technique suffers from a significant performance loss due to the range dependence of clutter. Here, an efficient clutter suppression approach is presented to improve STAP performance. Utilising the characteristics of clutter, the near-range clutter, the major reason for the performance degradation, is extracted from raw returns using a specially designed oblique projector firstly, and then is mitigated by an adaptive beamformer estimated from the extracted components. Subsequently, an azimuth-Doppler STAP beamformer is employed to further suppress the residual clutter. To enhance the robustness of the approach, a simple steering vector calibration technique is taken into account. The proposed approach can eliminate the near-range clutter effectively, and therefore alleviate the clutter range dependence greatly. The STAP performance can be improved significantly. Simulation results demonstrate the effectiveness of the presented method.