We describe our Lunar Navigation Satellite System (LNSS) that was designed to provide the PNT service at the Lunar South Pole region. Our LNSS is composed of eight satellites deployed in two elliptical lunar frozen orbits (ELFOs) that are the medium lunar orbits (MLO). This constellation design was performed to satisfy our target horizontal accuracy at the South Pole that is less than or equal to 40m every single second. Using the simulated real-time GPS navigation accuracy for the satellite flying in the ELFO, that is, the estimation errors of 30m for the satellite position, 2.62 × 10?8 (s) for the satellite clock bias, and 1.49 × 10?10 (s/s) for the clock drift, the satellite orbit and clock information was predicted by assuming the rubidium clock stability. Using these predicted results, we show that the our LNSS is capable of achieving the challenging horizontal positioning accuracy at the South Pole region.