Abstract: Adaptive digital beam forming is a fusion of antenna technology and digital signal processing, which has become a hot research topic in the cross domain, and widely used in the new generation of phased array radar and mobile communication. In this paper, an adaptive beamforming algorithm based on matrix manifold theory is proposed. Different from the traditional beamforming algorithms, this algorithm transforms the beamforming problem into a high dimensional optimization problem, and introduces the theory of the optimization of the matrix to solve the problem on the Stiefel manifold. Because the dimension of solving problem is reduced and the range of the optimal solution is limited, compared with the traditional adaptive beamforming algorithms, the proposed algorithm has the advantages of fast convergence speed, small computation quantity and good robustness.