A modified helical phase is presented in this paper. The generated vortex beams with the modified helical phases are characterized with ring-broken intensity distributions. The transverse intensity patterns of the generated vortex beams at a defined axial position and the focal plane are analyzed, respectively. The results demonstrate that the generated beam has an opening, whose size can be customized with a variable l′. The proposed vortex beams realized optical guiding of microparticles in the transverse planes of the beams. This kind of ring-broken beams will be promising for optical manipulation.