The primary aims of the BESS-Polar program are precise measurements of the low-energy antiproton spectrum and search for cosmologically significant antimatter, which would provide new clues to understand the early Universe. The second flight (BESS-Polar II) over Antarctica was successfully carried out in Dec 2007 - Jan 2008. We performed 24.5days scientific observation just at the solar minimum. The payload worked well during the flight and 4.7 billion cosmic-ray events were collected. Based on the BESS-Polar II data, we present recent preliminary results of cosmic-ray antiproton measurements and sensitive search for antimatter.