We present an axially asymmetric steady state model of Jupiter’s magnetosphere-ionosphere coupling with variable ionospheric conductivity dependent on the field-aligned current density. We use Juno and Galileo data to construct a simple model of the equatorial magnetic field, and develop a method for solving the system of partial differential equations describing magnetosphere-ionosphere coupling. Using this model we study the behavior of the system with different radial mass transport rates of magnetospheric plasma and the effect of additional field-aligned currents associated with Jupiter’s nightside partial ring current. We compare the model magnetodisc current intensities with those determined directly from magnetic field measurements in various local time sectors, and find that the value of mass transport rate of 2000 kg/s, larger than usually estimated, better accounts for the observed radial currents. We also find that the inclusion of field-aligned currents associated with Jupiter’s partial ring current helps to explain the local time variation of the radial currents, reducing the discrepancy between the model and the observations.