Porous structures have received a wide of attention in engineering applications, due to outstanding mechanical properties. However, the study on topology optimization for infill designs in porous structures considering the geometrical nonlinearity are in limited. In the work, the main intention is to propose a geometrical nonlinearity infill topology optimization method for the design of porous structures to achieve superior performance that can satisfy higher engineering demands. Firstly, the parametric level set method with numerical stability and high effectiveness is employed, where a boundary implicit description model is used for the representation of structural topology. Secondly, the constraint strategy is constructed for controlling the generation of local structural features using a modified Heaviside function, where local volume constraints for all finite elements are aggregated by implementing an upper limitation to generate porous infill pattern in design domain. Thirdly, the finite element formulation for geometrical nonlinearity in design domain is established using the Newton-Raphson method to solve unknown structural responses, subject to the large deformation assumption. Finally, numerical examples are tested to demonstrate the effectiveness and advantages of the proposed method through static analysis and comparisons of diverse design parameters.