we propose a non-paraxial hollow accelerating beam, which is formed by incoherently superposing two well-designed coherent accelerating beams. very interestingly, this incoherent superposition does not hamper the acceleration dynamics pertaining to the coherent ones, but results in a hollow intensity pattern in the cross section transverse to the circular accelerating trajectory. by a simple optimization, this hollow cross section pattern can be effectively extended to an angle close to 90 degrees. the magnitude and the phase of the angular spectrum of the beam are given followed by a suggested scheme to generate the beam in practice. such highly self-bending hollow beams may find applications in some fields such as optical manipulation. (c) 2016 optical society of america