For graphene to be used in semiconductor applications, a 'wide energy gap' of at least 0.5 eV at the Dirac energy must be opened without the introduction of atomic defects. However, such a wide energy gap has not been realized in graphene, except in the cases of narrow, chemically terminated graphene nanostructures with inevitable edge defects. Here, we demonstrated that a wide energy gap of 0.74 eV, which is larger than that of germanium, could be opened in uniform monolayer graphene without the introduction of atomic defects into graphene. The wide energy gap was opened through the adsorption of self-assembled twisted sodium nanostrips. Furthermore, the energy gap was reversibly controllable through the alternate adsorption of sodium and oxygen. The opening of such a wide energy gap with minimal degradation of mobility could improve the applicability of graphene in semiconductor devices, which would result in a major advancement in graphene technology.