This paper proposes a modified genetic algorithm that has the same beamforming performance and a fast convergence speed using general genetic algorithm in order to form a beam for the mobile node in a mesh network. The proposed beamforming genetic algorithm selects a part of chromosome a high fitness value in mating process to obtain fast convergence speed, and rest part of chromosome with longer fitness value in order to avoid local solution. Furthermore, the reference beam pattern with Gaussian shape reduces additional convergence speed. Simulation shows that the convergence speed of proposed algorithm improves 20% compared with that of conventional beamforming genetic algorithm.