We demonstrate an experimental setup for the production of a beam source of cold 87 Rb atoms.The atoms are extracted from a trapped cold atomic cloud in an unbalanced three-dimensional magneto-optical trap.Via a radiation pressure difference generated by a specially designed leak tunnel along one trapping laser beam,the atoms are pushed out continuously with low velocities and a high flux.The most-probable velocity in the beam is varied from 9 m/s to 19 m/s by varying the detuning of the trapping laser beams in the magneto-optical trap and the flux can be tuned up to 4×10 9 s-1 by increasing the intensity of the trapping beams.We also present a simple model for describing the dependence of the beam performance on the magneto-optical trap trapping laser intensity and the detuning.