While Type Ia supernovae (SNe Ia) serve as a powerful cosmological distance indicator, their nature remains unknown. Previous studies indicated that observations of SNe Ia discovered within a few days after the explosion (so-called early-phase SNe Ia) provide unique and robust constraints on their origins. Systematic studies of early-phase SNe Ia are now possible with the most powerful optical imaging survey instrument in the world — the Subaru Hyper Suprime-Cam (HSC). The MUlti-band Survey with the Subaru telescope for Early-phase SNe Ia (MUSSES) is a new project which aims to comprehensively investigate the early-phase photometric/spectroscopic behavior of SNe Ia with Subaru and other 2-10 m class telescopes around the world. During our first MUSSES observing run from April to June, 2016, several early-phase SNe have been successfully discovered. Moreover, we found a very interesting behavior in one of the light curves, whichis likely caused by the interaction between the SN ejecta and a companion star.