The possibility of a spin density wave (SDW) state in a metallic carbon nanotube (CN) and its electronic properties are investigated within the Hartree-Fock self consistent field (SCF) energy-band calculation. Two kinds of spatial SDW states are assumed in this study. Each assumed SDW on the wave function is constructed with the degenerate pi orbital in the metallic CN system, The results calculated for the one SDW model of CN always have a relative stability (similar to 0.1 eV/cell) in SCF total energy compared with the original model in which no SDW is assumed, All the results calculated for another SDW model are completely equal to the original one. Moreover, in the energy dispersion of the former stable SDW model, the degenerate pi level found in the original model disappears and the band gap (3-5 eV) occurs around at the Fermi level. The energetic stability and the band gap an also found in the pi-electron band calculation within the Hubbard Hamiltonian.