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Based on the derivative constraints, a reduced-rank cross-spectral metric (CSM) adaptive beamforming algorithm is proposed in this paper. In the proposed algorithm, the derivative constraints are firstly applied to impose a constrained band on the direction of expectation, and then the reduced-rank data is generated by using the reduced-rank adaptive signal processing based on CSM to generate the adaptive beamforming. The proposed algorithm is not only robust to the steering vector mismatch between the presumed and the actual array steering vectors, but also reduces the computational load significantly relative to the conventional robust adaptive beamforming algorithms. Simulation founds that the proposed algorithm can improve the performance significantly. [ABSTRACT FROM AUTHOR]