Existing reduced-dimension beam-Doppler space-time adaptive processing (RD-BD-STAP) algorithms are confined to the beam-Doppler cells used for adaptation, which often leads to some performance degradation. In this work, a novel sparsity-aware RD-BD-STAP algorithm, denoted Sparse Constraint on Beam-Doppler Selection Reduced-Dimension Space-Time Adaptive Processing (SCBDS-RD-STAP), is proposed can adaptively selects the best beam-Doppler cells for adaptation. The proposed SCBDS-RD-STAP approach formulates the filter design as a sparse representation problem and enforcing most of the elements in the weight vector to be zero (or sufficiently small in amplitude). Simulation results illustrate that the proposed SCBDS-RD-STAP algorithm outperforms the traditional RD-BD-STAP approaches with fixed beam-Doppler localized processing.