This paper presents a low-complexity robust data-dependent dimensionality reduction based on a modified joint iterative optimization (MJIO) algorithm for reduced-rank beamforming and steering vector estimation. The proposed robust optimization procedure jointly adjusts the parameters of a rank-reduction matrix and an adaptive beamformer. The optimized rank-reduction matrix projects the received signal vector onto a subspace with lower dimension. The beamformer/steering vector optimization is then performed in a reduced-dimension subspace. We devise efficient stochastic gradient and recursive least-squares algorithms for implementing the proposed robust MJIO design. The proposed robust MJIO beamforming algorithms result in a faster convergence speed and an improved performance. Simulation results show that the proposed MJIO algorithms outperform some existing full-rank and reduced-rank algorithms with a comparable complexity.