Electromagnetic (EM) field simulation plays a key role in the design of magnetic resonance imaging radio frequency (RF) coils. However, the values of the components in tuning and matching circuits often need to be iterated repeatedly in the conventional simulation method in order to achieve optimal scattering parameters. This leads to a time-consuming optimization to tune and match RF coils, particularly dual-tuned coils that are comprised of multiple lumped elements. A method combining EM field simulation and circuit simulation was employed in this paper, which can dramatically improve simulation efficiency for the optimization of the values of the lumped elements and corresponding EM field distribution. A systematical theoretical analysis of the co-simulation method was presented. To validate the accuracy and efficiency of the co-simulation method, a comparison study was conducted between the conventional simulation and the proposed co-simulation approaches.