The generation of fractional vortex beams and their propagation have been interesting research topics in recent years. In this paper we introduce a new type of fractional double-vortex beam, which is generated by the coaxial superposition of the vortex beams with two different fractional topological charges, and its total intensity distribution is of double-ring. We study the generation of this kind of beam theoretically and experimentally. It is shown that the rings of the fractional double-vortex beams carry different orbital angular momenta, from each other and propagate independently. The fractional double-vortex beams possess diverse manipulations as compared with the vortex beams with integer or single fractional charges. Therefore, the fractional double-vortex beam will be of great significance in optical rotation and manipulation of microscopic particles.