Based on the density functional theory, we calculate the band structure of an armchair carbon nanotube in an axial magnetic field. The result shows that there are two kinds of magnetic moments with different symmetries. One is the Aharonov Bohm-type magnetic moment which can be easily understood with classical picture, the other belonging to the valence, and conduction sub-bands should be explained by quantum mechanics. We use an effective mass model to analyse the magnetic moments and by comparing with the result of first-principle calculation, we conclude that the effective mass model is reasonable to estimate the change of the band gap in magnetic fields.