We use high-resolution angle-resolved photoemission spectroscopy (ARPES) and electronic structure calculations to study the electronic properties of rare-earth monoantimonides RSb (R = Y, Ce, Gd, Dy, Ho, Tm, Lu). The experimentally measured Fermi surface (FS) of RSb consists of at least two concentric hole pockets at the Γ point and two intersecting electron pockets at the X point. These data agree relatively well with the electronic structure calculations. Detailed photon energy dependence measurements using both synchrotron and laser ARPES systems indicate that there is at least one Fermi surface sheet with strong three-dimensionality centered at the Γ point. Due to the “lanthanide contraction”, the unit cell of different rare-earth monoantimonides shrinks when changing the rare-earth ion from CeSb to LuSb. This results in the differences in the chemical potentials in these compounds, which are demonstrated by both ARPES measurements and electronic structure calculations. Interestingly, in CeSb, the intersecting electron pockets at the X point seem to be touching the valence bands, forming a fourfold-degenerate Dirac-like feature. On the other hand, the remaining rare-earth monoantimonides show significant gaps between the upper and lower bands at the X point. Furthermore, similar to the previously reported results of LaBi, a Dirac-like structure was observed at the Γ point in YSb, CeSb, and GdSb, compounds showing relatively high magnetoresistance. This Dirac-like structure may contribute to the unusually large magnetoresistance in these compounds.