The electronic states of finite carbon nanotubes in the presence of electric and magnetic fields are calculated by the tight-binding model. Electronic properties such as state energy, energy gap, and density of states are mainly determined by the transverse electric field, the magnetic field, the Zeeman splitting, and the nanotube length, as well as the transverse geometric structure. The electric field could induce the destruction of state degeneracy, produce more low-energy states, and lead to significant changes in energy spacing. Complete energy-gap modulations exist during the variation of the electric field. Such effects are enhanced by the magnetic field.