An attractive specification of vertical axis wind turbine (VAWT) is its operating with wind at various directions. In order to achieve higher performance of these turbines, modeling of a curved-blade VAWT by the modified double multiple streamtube (DMST) method and optimizing this wind turbine are performed. Power coefficient and total normal force were selected as two objective functions. Then, a 3m height curved-blade VAWT type is optimized by Genetic Algorithm multi-objective optimization. Minimizing the normal force acting on turbine blades as the second objective function was not observed in open literatures. The amount of normal force is crucial in structural design of VAWT because it generates both the bending moment on blades and forces on supporting arms of VAWT. Another innovation of this study is to consider the shape coefficient parameter that determines the shape of the rotor geometry as a design variable in optimization procedure. Optimum values of design variables for the wind turbine were: selecting an elliptical rotor geometry, pitch angle -1.4º, diameter/height 1.3, blade aspect ratio 19.8 and tip speed ratio 4.3 and selecting three blades which could provide power coefficient of 0.49 and normal force of 158.7 N.