A KALIMER-600 concept which is a type of sodium-cooled fast reactor, has been developed at KAERI. It uses sodium as a primary coolant and is a pool-type reactor to enhance safety. Also, a supercritical carbon dioxide ($CO_2$) Brayton cycle is considered as an alternative to an energy conversion system to eliminate the sodium water reaction and to improve efficiency. In this study, a simplified model for analyzing the thermodynamic performance of the KALIMER-600 coupled with a supercritical $CO_2$ Brayton cycle was developed. To develop the analysis model, a commercial modular modeling system (MMS) was adopted as a base engine, which was developed by nHance Technology in USA. It has a convenient graphical user interface and many component modules to model the plant. A new user library for thermodynamic properties of sodium and supercritical $CO_2$ was developed and attached to the MMS. In addition, some component modules in the MMS were modified to be appropriate for analysis of the KALIMER-600 coupled with the supercritical $CO_2$ cycle. Then, a simplified performance analysis code was developed by modeling the KALIMER-600 plant with the modified MMS. After evaluating the developed code with each component data and a steady state of the plant, a simple power reduction and recovery event was evaluated. The results showed an achievable capability for a performance analysis code. The developed code will be used to develop the operational strategy and some control logics for the operation of the KALIMER-600 with a supercritical $CO_2$ Brayton cycle after further studies of analyzing various operational events.