This paper presents an investigation of the effect of steady and transient free-stream wind shear on the wake structure and performance characteristics of a horizontal axis wind turbine rotor. A new three-dimensional unsteady vortex-panel method potential flow solver based on a free-vortex wake methodology, AeroSIM+, is used for this purpose. The code is validated using the experimental data from the National Renewable Energy Laboratory Unsteady Aerodynamics Experiments. The effects of vortex core model, core size, expansion, and filament stretching on torque and thrust predictions are investigated. Three-different wind shear cases, i.e., uniform inflow (no wind shear), steady vertical wind shear that uses a power law velocity profile (Normal Wind Profile, NWP) and transient Extreme Wind Shear (EWS), are investigated. The results show that the existence of wind shear can create a very complex wake structure with substantial asymmetries, streamwise vorticity generation, and non-periodicities downstream of the turbine rotor. In addition, the blades are subjected to asymmetrical surface pressure variations that in turn result in high amplitude fluctuations in power and thrust levels generated by the turbine. Copyright (C) 2011 John Wiley & Sons, Ltd.