Through first-principles calculations, we report on the phonon-limited transport properties of two-dimensional (2D) hexagonal MSe (M = Ge, Sn, and Pb) compounds, which can be seen as a new family of 2D group-IV selenides established by the isovalent substitutions of germanium and tellurium in layered ${\mathrm{Ge}}_{4}{\mathrm{Se}}_{3}\mathrm{Te}$ phase [Angew. Chem. Inter. Edit. 56 10204 (2017)]. We find that 2D PbSe exhibits low values of sound velocity (800--2030 m/s), large $\mathrm{Gr}\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{u}}\mathrm{neisen}$ parameters $(\ensuremath{\sim}1.93)$, low-lying optical modes $(\ensuremath{\sim}20.02\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})$, and strong optical-acoustic phonon coupling. These intrinsic properties mainly stem from strong phonon anharmonicity, which greatly suppress the phonon transport and therefore give rise to an ultralow thermal conductivity $(\ensuremath{\sim}0.26\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1})$ for 2D PbSe at room temperature. Our studies may offer perspectives for applications of thermoelectricity and motivate further experimental efforts to synthesize MSe compounds.