A new kind of beam, i.e., power-exponent helico-conical (PEHC)optical beams, has been proposed in this paper. The proposed beams possess a variety of interesting properties different from optical vortex beams. The intensities of the proposed optical beams at the focal plane are analyzed theoretically and experimentally. The far field mappings are also theoretically analyzed. The results demonstrate that the proposed beams have the ring-broken openings which can be adjusted by modifying the exponent n. The proposed beams can be useful for the extension applications of helico-conical optical beams, especially for optical trapping, guiding, and sorting.