In a high pulse-repetitive-frequency forward-looking radar, the clutter echo is not only severely rangedependent but also range-ambiguous. It is therefore difficult to realize clutter compensation and suppression for conventional Space-Time Adaptive Processing (STAP) radar. To alleviate this problem, in this study, a novel range-ambiguous clutter suppression method is proposed for STAP radar with Frequency Diverse Array (FDA). Because the transmit steering vector of the FDA is range-angle dependent, the range-ambiguous clutter can be separated in the spatial domain using a subspace projection approach. The separated clutter can then be compensated using the Doppler warping technique. Finally, the compensated clutter can be suppressed, and target detection is realized in both the unambiguous and ambiguous range regions. Simulation examples demonstrate the effectiveness of the proposed method.