This paper presents a low-complexity reduced-rank approach to adaptive linearly constrained minimum variance (LCMV) beamforming. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of adaptive filters according to the minimum variance criterion. The constrained joint iterative optimization procedure adjusts the parameters of a bank of full-rank adaptive filters that forms the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe LCMV expressions for the design of the projection matrix and the reduced-rank filter and low-complexity stochastic gradient adaptive algorithms for their efficient implementation. Simulations for a beamforming application show that the proposed scheme outperforms in convergence and tracking the state-of-the-art existing reduced-rank schemes with significantly lower complexity.