The electronic properties of a nanotube–nanoribbon hybrid system are investigated by the first-principles calculations. This hybrid system is constructed by a zigzag carbon nanotube and an armchair graphene nanoribbon. Its electronic structures strongly depend on the nanotube location and stacking configuration. The interactions between the two subsystems would break the state degeneracy, open subband spacings, and induce more band-edge states. The predicted results could be measured directly by the scanning tunneling spectroscopy.