Abstract: In traditional beam-forming design of array antenna, the synthetic pattern of array antenna is obtained by weighting the radiation pattern of array element antenna with amplitude and phase. Usually, the weight of the amplitude and phase of the array element excitation depends on the comparison between the target pattern and the array synthesis pattern by the optimization algorithm. Because the algorithm is usually based on pattern-related array pattern, and the algorithm lacks side-lobe suppression mechanism, the pattern synthesis efficiency is not high and the side-lobe effect is usually unsatisfactory. In this paper, a direct synthesis algorithm of arbitrary beams is designed. First, a set of independent high gain narrow beams (free radical beams) is obtained based on the array element pattern, and then the direct synthesis of the beam pattern is carried out based on this beam. The problem of beamforming is unified, which avoids the random optimization of unknown parameters and greatly improves the efficiency of beamforming design of array antenna. Meanwhile, the sidelobe suppression mechanism is combined with the free Radix design, and the sidelobe suppression mechanism is independent from the beamforming process, so that the sidelobe of synthetic beams is natural, and it has the characteristics of low sidelobe.