Different dispersion near the electronic band edge of a semiconductor can have great influence on its transport, thermoelectric, and optical properties. Using first-principles calculations, it is demonstrated that a new phase of group-IV monochalcogenides (γ-MX, M = Ge, Sn; X = S, Se, or Te) can be stabilized in monolayer limit. γ-MXs are shown to possess a unique band dispersion-that is, camel's back like structure-in the top valence band. The band nesting effect near the camel's back region induces a large excitonic absorbance and significantly different exciton behaviors from other 2D materials. Importantly, the small effective mass and the indirect characteristics of lowest-energy exciton render it advantageous for the generation of electron-hole liquid state. After careful evaluation of the electron-hole dissociation temperature and the Mott critical density, it is predicted that a high-temperature exciton gas to electron-hole liquid phase transition can be achieved in these materials with a low excitation power density. The findings open up new opportunities for both the fundamental research on exciton physics and design of excitonic devices based on 2D materials with distinct band dispersion.