The design of superconducting magnets for a 600 kJ SEMS was discussed. The basic constraint conditions in the design of a 600 kJ SMES magnet were V-I loss(<1 W), inductance of magnet(<24 H), the number of Double Pancake Coils(DPC about 10), the number of turns of DPC(<300), outer diameter of DPC(close to 800 mm) and total length of HTS wire in a DPC(<500 m). As a result of optimum design, we obtained design parameters of the 600 kJ SMES magnet with two operating currents, 360 A and 370 A, which are in the limited conditions without V-I loss. V-I loss of each operating current was calculated with design parameters and V-I characteristic of the HTS wire. As a result of calculations, V-I losses with operating currents of 360 A and 370 A were 0.6 W and 1.86 W, respectively. Even though all design parameters of the SMES magnet in case of operating current of 360 A were in the restricted conditions, V-I loss of SMES magnet showed a tendency to generate at local DPCs, which are located on the top and the bottom of the SMES magnet more than that of the other DPCs.