A variable camber morphing rotor blade with curvilinear fiber composite skin is studied in this paper. The benefits of curvilinear fiber (CVF) composites for morphing skin over the linear fiber are investigated, initially. The skin of a morphing blade is modeled as a plate supported between the D-spar and trailing edge of typical rotor blade dimensions. The CVF composite shows about 60 % increase in the in-plane to out-of-plane bending deformation ratio compared to composites with linear fiber paths. In the second step, a previously developed biologically inspired variable camber internal structure is investigated for variable camber rotor blade. A fluid-structure interaction simulation is performed to obtain the aerodynamic loads acting on the skins of the variable camber internal structure proto type model. The upper skin of this prototype is modeled and optimized to find the optimal curvilinear fiber paths. The ply angles between the stringers are optimized to minimize the strain energy required to deform the skin for camber change and minimize the maximum out-of-plane deflection. The optimal results show that the plies which are away from neutral axis play a significant role in minimizing the out-of-plane deflections. The plies near to the neutral axis play a considerable role in minimizing the strain energy. Further, the skin requires the stiff plies near the D-spar and a flexible plies near the trailing edge tip as the pressure load decreases from the quarter chord to trailing edge portion of the airfoil. The numerical results show that the CVF composite skins can decouple the in-plane and out-plane requirements of morphing skins. The CVF composite skins show considerable reduction in the actuation energy while simultaneously minimizing the skin out-of-plane deformation requirements.