Abstract: The use of maximally sparse array to achieve the desired radiation pattern is a key problem in sparse array synthesis theory. Since the array antenna has intrinsic character of sparsity, the sparse array synthesis problem can be seen as a process of sparse signal reconstruction. In this paper, the problem of beamforming with antenna array is proved to be the same as the optimization problem of solving sparse signal vector. By using the focal undetermined system solver (FOCUSS) algorithm, maximally sparse array as well as the elements' locations and amplitudes are achieved quickly and accurately. The efficiency of this method is proved by theoretical analyses and numerical simulations.