Recently, the generalized eigenspace-based beamformer (GEIB) has been proposed to combat the pointing errors and to enhance the convergence speed. The weight vector of the GEIB is generated by projecting the weight vector of the linearly constrained minimum variance beamformer (LCMVB) onto a modified signal subspace. Unfortunately, numerical instability and high computational complexity have prohibited the GEIB from practical applications. In the paper, we propose the transformation-based adaptive array beamforming to overcome those problems. With the introduction of the transformation matrix, we first present an equivalent structure of the LCMVB. Based on the proposed LCMVB structure, the transformation-based GEIB is further developed without computing the modified signal subspace. With the removing of the computation of the modified signal subspace, the transformation-based GEIB becomes numerically stable and computationally efficient. Computer simulations are also given to demonstrate the correctness and usefulness of the transformation-based adaptive array beamforming.