Supercritical water-cooled reactors (SCWR) are one of the six types of nuclear reactors proposed by the Generation IV International Forum (GIF), which are basically light water reactors (LWR). SCWRs are specifically designed to remove heat from the core using the natural circulation system, a routine which is usually done by active pumps, while making the reactor functions safer. Since the conditions in the quasi-critical region are complicated for fluid like water, and the results of experiments and analyzes indicate discontinuities or extreme changes in various physical properties of water, the employed model tries to study the thermo-hydraulic properties and mass fluxes in the transient state. The computational model begins with the determination of the conservation equations (mass, energy, and momentum) for the nodes considered. In the model of the study of thermo-hydraulic properties, the discretization operations are performed after the formulation of conservation equations. Steady-state equations are next solved. Then, in order to investigate the mass flux in the transient conditions of the constant solution, we observe the mass flow fluctuation and fluctuations with the dependence of the mass flux on time.