We present an unbalanced three-dimensional(3D) magneto-optical trap(MOT) setup for the production of a continuous source of cold 87Rb atoms,which is cooled,trapped and pushed out by the MOT-generated radiation pressure difference employing a specially designed leak tunnel along one trapping laser beam.The coherence of the atomic beam is calculated with the velocity and the velocity spread which are obtained from the time-of-flight(TOM) signal.The experimental results show that an 87Rb beam with De Broglie wave length of 0.4 nm and bandwidth of 0.1 nm according to the most probable velocity of 12 m/s and a velocity spread of 3 m/s is generated with this method.And a flux of 108-109 atoms/s can be generated based on the measurement of the photomultiplier tube(PMT) signal from the source.