Low-energy electronic properties of carbon nanotubes subject to the influences of a transverse electric fieldand a magnetic field with angle α are studied by the tight-binding model. The external fields would modulateenergy dispersions, alter energy gaps, destroy state degeneracy, and create additional band-edge states. Thesemiconductor-metal transition is predicted for type-I and type-III nanotubes at all α’s, while it only occurs atcertain α’s for type-II nanotubes. The effects of external fields on the band structures are also directly reflectedin the density of states (DOS). The numbers, the heights, and the positions of the DOS divergent peaks arestrongly dependent on the external fields. Furthermore, the evolution of the DOS peak positions with theelectric field strength is also investigated.