Two-dimensional flows around a wind turbine of cross-flow are investigated by the numerical simulation. Incompressible Navier-Stokes equation is used for this simulation. A rotating coordinate system, which rotates at the same speed of the turbine, is used in order to simplify the boundary conditions on the blades of the turbine. Additionally, a boundary fitted coordinate system is employed in order to express the shape of the blades precisely. The third order upwind scheme is chosen for the approximation of the non-linear terms. Numerical simulations are also carried out by changing their shapes and angle of attack in order to estimate these effects on the performance of this turbine.