Actuator disc models are frequently used to provide a semi-analytical approach to estimating aerodynamic loads on rotary blades. The basic idea is to distribute the aerodynamic loads on a virtual rotating disc instead of simulating the actual rotating blade. These loads are then imposed to represent the source terms of the Navier-Stokes equations, which can be solved numerically using the computational fluid dynamic methods. The thickness of the actuator disk grid is one important factor considerably affecting calculations of the wind turbine rotor. Past researches generally considered the idea of fixed grid thickness exerting along the blade in their actuator disk modeling. However, this study introduces an innovative or improved actuator disk model, which takes into account the real blade thickness of a wind turbine in the computational fluid dynamic simulations. This novel actuator disk model is then incorporated into a finite-volume solver. This solver uses the second-order central and upwind schemes to approximate the diffusive and advective fluxes at the cell faces, respectively. The k-s turbulence model is used to close the turbulence closure problem. The NREL 5-MW wind turbine blade is chosen as a benchmark test to evaluate the results of the newly developed solver for the numerical predictions of the wind turbine rotor. The current study reveals that there is a specific fixed grid thickness value resulting in the most accurate predictions though with a much slower convergence rate. This specific value really depends on the chosen test cases and varies from one case to another. Its exact value may be found via try-and-error procedures, which would be computationally very expensive and time-consuming. Alternatively, this study introduces an improved actuator disk model capable of reinstating the real blade thickness in calculations. Subsequently, the wind turbine rotor performance is predicted numerically using both the improved and classic actuator disk models applying various fixed grid thickness values along the blade. The results demonstrate that the accuracy of the classic actuator disk model strongly depends on the grid thickness magnitude. On the contrary, the newly improved actuator disk model results in some solutions, which are as accurate as those of the most accurate classic actuator disk model, while suitably speeding up the convergence rate.