In this paper, a novel reduced-dimension approach to linearly constrained minimum variance beamforming is investigated. The proposed method is able to achieve a LCMV solution through a number of optimization cycles based on the partition matrices of small sizes instead of a full dimensional correlation matrix. The problem is formulated as a conditional optimization problem. The derivations and equations for the proposed method are shown. The proposed method achieves the optimal performance with a fast convergence and a stable performance characteristic. Simulation results illustrate the effectiveness of the proposed method.