A new type of the double-vortex beam is generated by the coaxial superposition of vortex beams with two different topological charges, whose intensity distribution is double-ring. The propagation characteristics of this kind of beams theoretically and experimentally are studied. It is found that each ring of the double-vortex beam carries different orbital angular momentum, and is propagating independently. In addition, when the internal topological charge of the double-vortex beam remain unchanged, the distance between the two rings of the double-vortex beam gets bigger with increasing the external topological charge.