The Reaktor TRIGA PUSPATI (RTP) rely extensively on a core power control system for control reactivity to fulfilment the fundamental safety function for a nuclear reactor. It is technically challenging to operate within tight multiple parameter constraints and keep the core power output stable. At present, the power tracking performance of the system could be considered unsatisfactory which produces a relatively long settling time and high control effort. Hence, a study of a model predictive control (MPC) strategy by integrating the current Power Change Rate Constraint (PCRC) using fuzzy logic which is part of the core power control design is conducted. In this paper, the MPC design based on mathematical models of the reactor core included point kinetics model, thermal-hydraulic model, reactivity model and dynamic rod position model help to enhance core power control. The power tracking performance of the proposed control method and previous Feedback Control Algorithm-Fuzzy PCRC is compared via computer simulation with different power range operations. Overall, the results show the MPC-Fuzzy PCRC strategy provides a greater level of operational safety and optimum operation of the TRIGA reactor.