The structural and electronic properties of a hybrid of an armchair graphene nanotube and a zigzag graphene nanoribbon are investigated by first-principles spin-polarized calculations. These properties strongly depend either on the nanotube location or on the spin orientation. The interlayer spacing, the transverse distance from the center of the ribbon and the stacking configuration affect the electronic structures. The antiferromagnetic configuration has a lower total energy than the ferromagnetic one. The interlayer atomic interactions between the two subsystems would change the low energy dispersions, open subband spacings, and induce more band-edge states. Moreover, such interactions create an energy gap and break the spin degeneracy in the antiferromagnetic configuration. The band-edge-state energies are sensitive to the nanotube location.