By using two-dimensional particle-in-cell simulations, we demonstrate high-flux dense positrons generation by irradiating an ultra-intense laser pulse onto a tapered hollow target. By using a laser with an intensity of 4×1023W/cm2, it is shown that the Breit-Wheeler process dominates the positron production during the laser-target interaction and a positron beam with a total number >1015 is obtained, which is increased by five orders of magnitude than in the previous work at the same laser intensity. Due to the focusing effect of the transverse electric fields formed in the hollow cone wall, the divergence angle of the positron beam effectively decreases to ∼15° with an effective temperature of ∼674MeV. When the laser intensity is doubled, both the positron flux (>1016) and temperature (963MeV) increase, while the divergence angle gets smaller (∼13°). The obtained high-flux low-divergence positron beam may have diverse applications in science, medicine, and engineering.