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In this work, a constrained adaptive filtering strategy based on conjugate gradient (CG) and set-membership techniques is presented for adaptive beamforming. A constraint on the magnitude of the array output is imposed to derive an adaptive algorithm that performs data-selective updates when calculating the beamformer's parameters. A linearly constrained minimum variance optimisation problem is consider with the bounded constraint based on this strategy and propose a CG-type algorithm for implementation. The proposed algorithm has data-selective updates, a variable forgetting factor and performs one iteration per update to reduce the computational complexity. The updated parameters construct a space of feasible solutions that enforce the constraints. The authors also introduce two time-varying bounding schemes to measure the quality of the parameters that could be included in the parameter space. A comprehensive complexity and performance analysis between the proposed and existing algorithms are provided. Simulations are performed to show the enhanced convergence and tracking performance of the proposed algorithm as compared with existing techniques.