A new type of composite vortex beam was generated by the coaxial superposition of two high-order radial Laguerre-Gaussian beams with the same radial indices and opposite topological charges. The intensity distribution characteristic and space propagating property of composite vortex beams were studied theoretically and experimentally. The results show that the composite vortex beam, which is superimposed by the high-order radial Laguerre-Gaussian beam, has a multi-layer bright "petal"; When the beam waist radius are same, with the increase of propagation distance, the intensity distribution of the beam spreads but does not rotate; When the waist radius are different, the intensity distribution rotates, and the phenomenon of "rotating tail" appears. The rotating direction and "trailing" direction depend on the number of topological charges and the size of the waist radius. The results provide an experimental basis for understanding the generation of composite vortex beam and further extending its application scope.