In recent years, machine learning methods have been widely used in modeling material behavior. In this work, a novel neural network-based method for simulating the complex nonlinear relations of porous solid materials is proposed. To achieve this objective, an artificial neural network is used to learn path-dependent inelastic behavior of porous material. The network is constructed utilizing a general internal variable formalism, with the number of internal variables being dependent on the nature of the problem and the desired level of accuracy. The training data are generated with numerical multi-scale homogenisation based on an RVE composed of the von Mises elasto-plastic matrix with an arbitrary void volume fraction. The RVE numerical simulation was performed by enforcing the RVE's boundary conditions and the stress responses on macro scale are computed for various macro strain data sequences to generate different loading paths. The neural network based stress update algorithm is trained and validated. The obtained results show the potential of describing the material stress/strain relationship with high accuracy. In addition, the hydrostatic pressure and the norm of the deviatoric stress show accurate results when compared against the corresponding Gurson model for porous elasto-plastic material. Hence, the trained neural network model can be utilized in finite element based analysis to study real-world applications.