The field emission current from a carbon fiber is considered. As a model of emission of an elementary carbon tube, tunnel ionization of an electron from a short-range potential is taken. The exact solution for the wave function in such a model allows obtaining an asymptotic expression for electron current. A computer model of transverse distribution of emission current of a carbon fiber is built on the basis of the Monte Carlo method that allows taking into account the random character of distribution of local emitter sources and the distribution of gains of an electric field in carbon nanotubes.