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A new generalized sidelobe canceller (GSC) based minimum variance distortionless response (MVDR) beamformer is proposed in this paper, which applies constrained stability least mean squares (CS-LMS) algorithm for adaptive weights optimization. With a different recursive formula, CS-LMS algorithm is more flexible than normal LMS algorithm. Then, this algorithm is introduced into GSC based MVDR beamformer. As a result, a good signal of interest (SOI) extraction and interferences nulling performance is obtained. Simulation experiments show the merits of the proposed beamformer against the other two, GSC based MVDR beamformer with LMS algorithm and fully adaptive MVDR beamformer.