<p>Fiber-reinforced composites have been widely applied in large deformation engineering structures. To further enhance the designability of fiber-reinforced composites, this paper proposes a novel method for concurrent topology optimization of fiber orientation and the material distribution considering geometric nonlinearity. The fibers and matrix are modeled independently using the membrane-embedded model. A concurrent optimized interpolation scheme for the membrane-embedded model is constructed for geometrical nonlinearity. The concurrent topology optimization model for composite under double volume constraints is proposed to achieve an optimal balance between structural stiffness and material usage. The sensitivities of the design variables for the two materials are derived by the adjoint method, respectively. Numerical examples obtain different optimization results for different magnitude forces, fiber contents and fiber—matrix stiffness ratios. This demonstrates that the proposed method effectively enhances the designability of composites under large deformations.</p>