Abstract: The beam transport system of the Dragon-Ⅰ linear induction accelerator(LIA) consists of hundreds of solenoid coils and dipole steering coils, which are designed to reduce corkscrew amplitude and transverse motion of electron beam. In order to improve the beam quality, a genetic optimization model of solenoid currents is proposed in this paper and the optimization code GABC based on genetic algorithm and beam transport models is designed, which contains both beam centroid track and the beam envelope model. The matched magnetic field in five blocks of the Dragon-Ⅰ LIA, including twenty induction acceleration cells and five connection cells, are analyzed using the optimization code. The numerical results reveal that the GABC is effective to solve transport magnetic field optimization problems and could play an important role for beam tuning simulation and experiment.