The MeV gamma-ray domain is the only unexplored window among recent multiwavelength observations in astrophysics, often referred to as the "MeV gap". To bridge this gap, there are several ongoing and planned projects of MeV gamma-ray telescopes. The measurement of MeV gamma rays (both continuum and line emission) would give us new insight into many topics in astrophysics, such as studies of relativistic jets, particle acceleration, and origin of matter. In advance of the future missions, we have been working on prediction of the MeV gamma-ray sky, which is helpful to determine what kinds of sources can be detectable with the future telescopes. In order to explore MeV gamma-ray sources, we performed a catalog cross-matching between the hard X-ray (Swift-BAT) and GeV gamma-ray (Fermi-LAT) catalogs, resulting in 145 firmly cross-matched sources. Most of the sources are brighter than 10$^{-11}$ erg/cm$^2$/s in the 1-10 MeV band and thus promising targets for future observations. Combined with the Galactic diffuse and extragalactic emission, the all-sky maps in the MeV gamma-ray band can be produced. We find that it is dominated by the Galactic diffuse emission at lower latitudes, while the extragalactic component becomes dominant at higher latitudes. This all-sky study is also used to investigate a long-standing problem in MeV gamma-ray astrophysics: the origin of the diffuse emission from the inner Galaxy, measured by COMPTEL. I will report analysis and results in detail and introduce future missions for MeV gamma-ray observations.