A novel STAP algorithm based on sparse recovery technique, called CS-STAP, were presented. Instead of using conventional maximum likelihood estimation of covariance matrix, our method utilizes the echo statistics on spatial-temporal plane, which is extracted from sample data of only ONE training range cell with Compressed Sensing techniques, to construct a new estimator of covariance matrix, and build the optimal detector based on it. Full description of CS-STAP is given. Numerical result on real data has provided the evidence for great potential of CS-STAP as a effective approach when clutter is non-stationary because it need much less training data compared with common STAP methods.