Frequency diverse array (FDA), which employs a small frequency increment across the array elements, is able to resolve range ambiguity. However, the frequency diversity results in angle-Doppler-defocusing of target especially at a high speed in space-time adaptive processing (STAP) radar, thus, causing serious detection performance degradation. In this paper, a robust adaptive beamforming approach is proposed for the FDA-STAP radar to enhance fast-moving target detection performance. In our solution, a large feasible region is employed to include the true steering vector of target. To avoid the trivial solution, an angle-Doppler-defocusing steering vector constraint is devised and incorporated into the large feasible region. The problem is formulated as a nonconvex quadratically constrained quadratic program which is efficiently solved via semidefinite relaxation technique. Because the retrieved steering vector of target is close to the true one, the performance is significantly improved. It is demonstrated via computer simulations that the proposed algorithm is superior to the state-of-the-art methods, which includes maintaining the mainlobe of the beampattern and improving the signal-to-clutter-plus-noise ratio performance.