We consider a system of liquid crystal modeled by hard spherocylinders. In certain range of the pressure, the system exhibits two metastable phases: the isotropic phase and the nematic phase. In the isotropic phase, the spherocylinders are randomly packed. In contrast, the spherocylinders are well-ordered in the nematic phase. The isotropic-nematic phase transition is a rare event because it involves the crossing of energy barrier(s). This makes direct simulations, e.g. using molecular dynamics, of the transition event infeasible. In this paper, we study the phase transition in a coarse-grained space formed by two collective variables: the order parameter of the spherocylinders and the volume of the system. We compute the free energy in the collective variable space, the minimum free energy path (MFEP) between the isotropic phase and the nematic phase, and the transition state. Our results reveal the multilayer structure of the critical nucleus. The nucleus will grow further and evolve to the nematic phase after it crosses the energy barrier.