Abstract：In the field of precision measurement and aerospace, atomic gyroscope and atomic magnetometer have high requirements on the uniformity of magnetic field, while the uniformity of magnetic field generated by the traditional Helmholtz coil is not good enough for these applications. To obtain better field uniformity, a method to calculate the parameters of cylindrical coil systems is proposed, based on the Taylor expansion of the axial magnetic field. The parameters of two- to nine-coil systems are computed, and the trends of magnetic field uniformity, coils’ size, and coils’ maximum ampere-turn ratio with coil number are analyzed. Numerical results demonstrate that the uniform region area of magnetic field increases almost linearly with the increasing of coil number, and the region area where the field uniformity is better than 0.01% in nine-coil system is about 30 times as larger as that in Helmholtz coil. A method of rounding coil ampere turns ratio is presented when integer coil turns and the same current in each coil turn are required, and the integer ampere turns ratio of two- to nine- coil systems are given. Numerical results show that the uniformity of our coil systems is better than those in other papers.