As a class of graphene-like two-dimensional materials, the layered metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te) have gained significant interest due to the indirect to direct bandgap transition and rather large exciton binding energy in monolayer limit. Both the direct bandgap and strong exciton binding energy make monolayer MX2 favorable for optoelectronic applications. Furthermore, the two energy degenerate valleys of both the conduction and valence bands at corners of the first Brillouin zone bring MX2 the possibility of valley-based electronic and optoelectronic applications. Using molecular beam epitaxial (MBE) method, we achieved layer-by-layer growth of high-quality single-crystal MoSe­2 thin film. Our in-situ angle-resolved photoemission spectroscopic (ARPES) study directly revealed the bandgap transition and band structure evolvement with different film thickness from one monolayer (ML) to 8 ML. Combining with further photoluminescence (PL) spectroscopy, scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS), we experimentally found a rather large exciton binding energy (~0.5eV) in monolayer MoSe2, which demonstrate an enhanced many-body effects in such 2D system. Moreover, we observed a significant band splitting of ~180 meV at valence band maximum of a monolayer MoSe2, which was theoretically predicted to be 100% spin-polarized. This spin signature gives the layered MoSe2 another application potential in spintronic devices, as well as a new playground to investigate spin-obit physics beyond the topological insulators.