A flat distribution of the minimum magnetic field (flat-Bmin) of an electron cyclotron resonance ion source (ECRIS) is expected to perform better in highly charged ion production than classical Bmin. To form a flat-Bmin structure with a liquid helium-free superconducting device, a coil system of seven coils with four current leads has been designed. The lead number was reduced by connecting the plural coils in series to maintain the flat-Bmin structure even when the coil currents are changed for adjustment. This coil system can be operated with a helium-free cryostat, since the estimation of heat from the leads to the coils is nearly equivalent to the existing superconducting ECRIS of a similar type.