The design of a superconducting magnet system producing very high magnetic field is underway at Korea Basic Science Institute (KBSI) to accelerate three kinds of carbon irons (C+2, C+4, C+6) to 120 MeV. A quarter-scaled prototype will be manufactured in order to confirm the feasibility of our design. Magnet Inductances in the system have a great influence on the current ramping rates and contribute to the stored energy, which are usually considered to be unfavorable in magnet operation. The modeling and simulation scheme of a prototype superconducting magnet for the cyclotron K120 is described in this paper. The inductances are calculated by a numerical method with and without iron yokes, respectively. These calculation results will be used as engineering design details such as a current ramping rate and a quench protection design.