The high-temperature gas cooled-reactor (HTGR) has been constructed in Japan and produces rated power operation and hydrogen, contributing to the development of future energy strategies. One type of HTGR, the high-temperature engineering test reactor (HTTR), uses long hexagonal fuel assemblies. The HTTR is a graphite-moderated, helium-gas-cooled reactor with thermal power of 30 MW, an inlet coolant temperature of 395° C, and an outlet coolant temperature of 950° C. In this paper, a nonlinear mathematical model of the nuclear reactor core was derived in derivative form using fundamental principles. Unknown parameter data could be estimated with physics equations using the nonlinear least squares curve fitting method. The validation between the mathematical model and experimental data of the plant-obtained simulation response indicates that the model could have been used for further optimization and control. The simulation-response results showed that the mathematical model with estimated parameters has an accuracy above 89%. Consequently, based on the simulation response, the mathematical model could be used as the HTTR continues to function.