In this thesis, a concept design of supercritical $CO_2$ cooled KAIST Micro Modular Reactor (KAIST MMR) was proposed. The KAIST MMR contains a long-life core, a passive decay heat removal system, and a su-percritical $CO_2$ power cycle in one transportable module. A three-dimensional computational fluid dynamics (CFD) analysis was performed to improve the design methodology of a supercritical $CO_2$ (S-$CO_2$) compressor. Accurate properties for S-$CO_2$ was implemented to the CFD code. From the observation of previously ob-tained experimental results, it was recognized that the amount of external losses in the secondary flow paths can be substantial. Understanding the external loss mechanisms, and reducing the external losses are critical to the design of a high performance S-$CO_2$ compressor. Therefore, this study first focused on the selecting an appropriate external loss model by estimating the internal loss accurately through a high fidelity CFD calcula-tion and then substituting from the total losses. By analyzing the CFD result and energy balance data ob-tained from the experiment, this study suggests the best combination of the previously developed external loss models for the $S-CO_2$ compressor design and performance prediction. This is followed by the investiga-tion of the condensation effect in the impeller by utilizing a two-phase VOF model with metastable properties. As a result, it is re-confirmed that there is a negligible amount of condensation effect. In addition, the analysis models with various number of blades are tested with the CFD, and the optimal number of blades was deter-mined. Moreover, a structural analysis for one-blade-set model was conducted to examine if thinner blade can be used. As a result, the reduced blade thickness still can endure the stress caused by the pressure load. The new findings from this study were applied to the 1D meanline turbomachinery design code, KAIST-TMD. A new S-$CO_2$ compressor for KAIST MMR was designed based on the updated design code. The new design has characteristics of reduced external losses and optimized number of blades to achieve higher efficiency and pressure ratio than those of the old design.