This article presents the assessment of the power coefficient of a small three-bladed H-type Darrieus wind turbine when using modified non-symmetrical airfoil profiles: LS(1)-0413-Mod-4 and S813-Mod-5, at a low wind speed of 5 m/s. For this purpose, the configuration parameters of the turbulence model, computational domain, and meshing have been obtained by reviewing the state of the art about Computational Fluid Dynamics (CFD) simulations with the software ANSYS-Fluent in order to select the best airfoil profile for the wind turbine. Additionally, the effect on the performance of the power coefficient (cp) of the turbine has been studied for a fixed pitch angle in a range between -5 ° and 2°. An analysis of the effect on the cp has been also made when the blade-spoke connection point has been at 25% or 50% of the chord line. Finally, with the best configuration between the non-symmetrical airfoil profile, pitch angle, and blade-spoke connection point, the turbine performance has been simulated at a range of different speeds: from 3 m/s to 18 m/s. Consequently, the maximum power of the turbine has been estimated according to different wind speeds.