An inner plunger of a solenoid coil assembly for a differential clutch of a vehicle contributes to weight lightening and price reduction of a solenoid assembly, provide various shapes, reduce friction against an inner housing, and improve the function of the solenoid assembly. The inner plunger includes an outer wheel combined with a coil bobbin of a solenoid assembly and an inner wheel combined with an inner housing. The inner wheel is molded of insulator synthetic resin with excellent moldability, magnetic metal as the outer wheel is inserted into the outer circumferential surface of the inner wheel made of the synthetic resin, a retaining groove formed in the outer wheel is filled with the synthetic resin of the inner wheel, and a support piece formed on the inner wheel supports the outer wheel.