Axons as microstructural constituent elements of brain white matter are highly oriented in extracellular matrix (ECM) in one direction. Therefore, it is possible to model the human brain white matter as a unidirectional fibrous composite material. A micromechanical finite element model of the brain white matter is developed to indirectly measure the brain white matter constituents’ properties including axon and ECM under tensile loading. Experimental tension test on corona radiata conducted by Budday et al. 2017  is used in this study and one-term Ogden hyperelastic constitutive model is applied to characterize its behavior. By the application of genetic algorithm (GA) as a black box optimization method, the Ogden hyperelastic parameters of axon and ECM minimizing the error between numerical finite element simulation and experimental results are measured. Inverse analysis is conducted on the resultant optimized parameters shows high correlation of coefficient (>99%) between the numerical and experimental data which verifies the accuracy of the optimization procedure. The volume fraction of axons in porcine brain white matter is taken to be 52.7% and the stiffness ratio of axon to ECM is perceived to be 3.0. As these values are not accurately known for human brain white matter, we study the material properties of axon and ECM for different stiffness ratio and axon volume fraction values. The results of this study helps to better understand the micromechanical structure of the brain and micro-level injuries such as diffuse axonal injury.