An adiabatic demagnetization refrigerator (ADR) is numerically investigated to predict the cooling performance below 4.5 K. The proposed system consists of helium thermosyphon for the warm side heat switch and a magneto-resistive tungsten for the cold side heat switch. Gadolinium Gallium Garnet (GGG) is selected as magnetic material. By adapting appropriate heat switching method for the warm and the cold sides, the passive operation of heat switches is feasible. The numerical analysis is conducted with the 1-dimensional heat diffusion model considering thermal contact resistance in ADR. Homogeneous model is applied on the thermosyphon heat switch. The calculation results show that the ADR can produce cooling capacity of 0.770 J at 2 K when the temperature of the warm end is maintained as 4.5 K. COP of the ADR is predicted as 0.376. The detailed design methodology and the results are presented and discussed.