The effects of the external magnetic field on the energy gap of carbon nanotubes were investigated by using the tight-bonding method. It was found that, under the applied magnetic field, the peak of energy gap induced by magnetic field and the slope of energy gap versus magnetic field depend on their diameters tightly; when tubes with the same diameters are used, the metal type tubes have the highest energy gap peak. Furthermore, under the magnetic field, the density of states of carbon nanotubes near the Fermi level are also calculated, showing that the Van Hove singularities will exhibit a periodic phenomenon of splitting, moving and merging. Our calculations meet the results from Green's function method, so they are reasonable.