Anisotropic semi-Dirac materials exhibit unique manipulation selectivity in carrier conduction. Currently, the behavior of semi-Dirac electrons has been successfully observed in black phosphorus thin films and topological metal ZrSiS materials. This behavior manifests as linear and parabolic dispersion relations along two mutually perpendicular high-symmetry paths near the semi-Dirac point. Based on first-principles calculations, it is predicted that semi-Dirac electronic states can be realized in the structural system of anisotropic stacked graphene nanoribbon arrays on a graphene substrate in this work. The effects of nanoribbon width, the ratio of graphene width to nanoribbon width in the supercell, and external electric field on this semi-Dirac system band are further investigated. It is worth noting that the processes of the conduction band and valence band transitioning from non-conical-contact to conical-contact under an applied perpendicular electric field to form the semi-Dirac point are analyzed through computational simulation. Correspondingly, the system transforms from a metal with direction-dependent flat bands near the Fermi level to a direct bandgap semiconductor. The research provides theoretical reference for realizing and tuning semi-Dirac electronic states in two-dimensional material nanostructures.