Transcritical and supercritical fluids widely exist in aerospace propulsion systems, such as the coolant flow in the regenerative cooling channels of scramjet engines. To numerically simulate the coolant flow, we must address the challenges in solving Riemann problems (RPs) for real fluids under complex flow conditions. In this study, an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed. Due to the comprehensive resolution of fluid thermodynamics, the proposed solution framework is suitable for all forms of the two-parameter equation of state (EoS). The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points. Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids, ensuring that the same mathematical properties as ideal gas could be applied in Newton’s iteration. A series of numerical cases validate the effectiveness of the proposed method. A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS, the ideal gas EoS, and the improved ideal gas EoS under supercritical and transcritical conditions. The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.