A Zeeman slower is taken as the cooling device for Sr atomic beam injected into the magneto-optical trap (MOT). An efficient method for design and construction of the Zeeman slower,which calculated the coil distribution exactly matching the analytical magnetic field by computer program,is proposed. The flow chart and the algorithm structure of the optimization design program are illustrated in detail. The experimental magnetic field produced by Zeeman slower coils and the signal from magneto-optical trap (MOT) are measured. Based on the computer program simulation,the model can be flexibly adjusted according to the experiment. The coil distribution can calculated by matching the change of parameters and analytical magnetic field. The RMS value between calculated field and analytical field is 2.17×10-4 T.