By utilizing the holographic technique, a novel type of twins composite discrete Airy-vortex accelerating beam is generated with discrete Airy-vortex phase which is processed by binary phase. The propagation properties of the accelerating beam and the modulation of different parameters [the linear factor(s)、the number of total layer (N) and the topological gradient (ΔL)]to the accelerating beam is also studied by theoretical simulation and experiment. The results show that such twins accelerating beam will split itself into several separated Airy-like beams due to the discrete and rotatory effect in propagation; and the separated Airy-like beams evolve into one-dimensional Airy-like beams by adjusting the propagation distance and ΔL. Furthermore, s and N can modulate the intensity distribution of twins accelerating beam and the space distribution of twins accelerating beam in initial plane (the plane x-y at z=0), respectively; ΔL also can modulate the intensity distribution of separated Airy-like beams.