The organic Rankine cycle (ORC)-based waste heat recovery (WHR) system operating under a supercritical condition has a higher potential of thermal efficiency and work output than a traditional subcritical cycle. However, the operation of supercritical cycles is more challenging due to the high pressure in the system and transient behavior of waste heat sources from industrial and automotive engines that affect the performance of the system and the evaporator, which is the most crucial component of the ORC. To take the transient behavior into account, the dynamic model of the evaporator using renowned finite volume (FV) technique is developed in this paper. Although the FV model can capture the transient effects accurately, the model has a limitation for real-time control applications due to its time-intensive computation. To capture the transient effects and reduce the simulation time, a novel fuzzy-based nonlinear dynamic evaporator model is also developed and presented in this paper. The results show that the fuzzy-based model was able to capture the transient effects at a data fitness of over 90%, while it has potential to complete the simulation 700 times faster than the FV model. By integrating with other subcomponent models of the system, such as pump, expander, and condenser, the predicted system output and pressure have a mean average percentage error of 3.11% and 0.001%, respectively. These results suggest that the developed fuzzy-based evaporator and the overall ORC-WHR system can be used for transient simulations and to develop control strategies for real-time applications.