A new transient source was discoverd on 2018 December 21 by MAXI (Kobayashi+ ATel #12320). NuSTAR followup observations on December 28 revealed that the source was a new transient source, MAXI J1631-479, and the obtained 3-79 keV X-ray energy spectrum suggested that it was a black hole binary (Miyasaka+ ATel #12340). After the discovery, the source brightened gradually. In the initial stage of the outburst, the 2-20 keV GSC spectrum was discribed by a power-law model with a photon index of $\leq$ 2. After December 25, the spectrum was discribed by a disk-blackbody plus power-law model. After 2019 January 7, the spectrum was dominated by a disk-blackbody component with a constant inner disk radius, and in a few days the 2-10 keV X-ray flux reached the peak value of about 2 Crab. After the peak flux, the source dimmed gradually, and made a transition to the hard (intermediate) state on January 23 (Negoro+ ATel #12421), where the spectrum was discribed by a disk-blackbody plus power-law model. In March, it came back to the soft state again. On June 4, the source underwent a soft-to-hard transition, and the spectrum was dominated by a power-law component. If a soft-to-hard transion occurs at 1-4% of the Eddington luminosity (e.g., Maccarone 2003), the source distance is estimated at about 10 kpc for a 10 solar mass black hole.