Issues of designing a single-stage high-loaded turbine of a marine gas turbine engine are considered. The object of our research is the aerodynamic characteristics of a viscous three-dimensional turbulent gas stream flow in the flow path of the turbine under consideration. At this stage, a numerical analysis of working processes in the blade passages of the turbine stage has been carried out. When designing the turbine, it is necessary to take into account the fact that the possibilities of improving the flow path shape by optimizing the shapes of blade passages in plane sections do not meet the requirements for high-loaded turbines. An alternative to this approach is the use of computational gas-dynamic methods in a three-dimensional formulation. Therefore, this paper outlines a method for constructing a refined finite element model of the working fluid flow in the flow path of the single-stage high-loaded high-pressure turbine of a marine gas turbine engine. To solve this problem, a finite-element hexagonal-type mesh was constructed using the three-dimensional Navier-Stokes equations for the case of viscous working fluid flow. The three-dimensional model of the turbine flow path presented in this paper consists of two stator sections and four rotor sections. Each section includes a blade airfoil with upper and lower contours, which simply model the root and shroud shelves. In the course of calculations, such types of boundary conditions as "entrance", "exit" and "wall" were used. At the entrance, the total flow pressure and flow temperature were given. Since the turbine is single-stage, then at the entrance to the computational domain, the flow is directed axially. At the exit from the computational domain, the static pressure was given. On the wall, both the non-slip and slip boundary conditions were also used. Using the developed mathematical model, the fields of Mach numbers, flow velocities, and static pressure in the root and peripheral sections of the turbine flow path are determined. The calculation was carried out in a non-stationary setting with a time step of 1.597410-6 s, which corresponds to the angle of rotor rotation, relative to the stator, of 0.09 degrees. The total number of time iterations was 200. The results obtained can be applied to further study the strength of the blading of highly-loaded marine gas turbine engines.