This paper introduces the flower pollination algorithm (FPA) as an optimization technique suitable for adaptive beamforming of phased array antennas. The FPA is a new nature-inspired evolutionary computation algorithm that is based on pollinating behaviour of flowering plants. Unlike the other nature-inspired algorithms, the FPA has fewer tuning parameters to fit into different optimization problems. The FPA is used to compute the complex beamforming weights of the phased array antenna. In order to exhibit the robustness of the new technique, the FPA has been applied to a uniform linear array antenna with different array sizes. The results reveal that the FPA leads to the optimum Wiener weights in each array size with less number of iterations compared with two other evolutionary optimization algorithms namely, particle swarm optimization and cuckoo search.