The method for calculating the field-emission current from single carbon nanotubes in an external electric field, directed along the nanotube axis, has been presented. The method is based on a semi-classical approach implementing the sub-barrier tunneling. It has been shown that in case of the high-fields the current corresponds to the Fowler-Nordheim mechanism for field emission, and in the case of the low ones - has deviations related to the potential barrier behavior feature.