The main purpose of this paper is to optimize winglet geometry by using CFD with Genetic Algorithm and study its effects on power production. For validation and as a baseline rotor, the NREL Phase VI wind turbine rotor blade is used. The Reynolds-Averaged Navier-Stokes equations are solved and different turbulence models including the Spalart-Allmaras, k-epsilon Launder-Sharma, k-epsilon Yang-Shih and SST k-omega models are used and tested. The results of the power curve and the pressure distribution at different spanwise sections of the blade are in good agreement with the experimental data especially for the k-epsilon Launder-Sharma. In the winglet design, the variable parameters are the cant and twist angles of the winglet. Multipoint optimization is carried out for three different operating wind speeds and 24 samples are obtained for each one. The final optimized winglet showed around 9% increase in the power production.