A two-stage dimension-reduced space-time adaptive processing (STAP) based on correlation matrix is proposed for clutter suppression and moving target detection. Firstly, to reduce the degrees of freedom of the clutter, the full dimensional space-time received data is pre-filtered. Secondly, the correlation matrix of output data after preprocessing is divided into submatrices, and further reduction of both the computational complexity and the training requirement is achieved by optimizing two low-dimensional weight vectors . Theoretical analysis and computer simulation results illustrate that the proposed method can obtain fast convergence and better clutter suppression performance. The method shows good robust performance with a small computational cost when there are clutter fluctuation and random amplitude and phase errors in array elements. Experiment results by using measured data demonstrate effectiveness and robustness of the proposed method.