The essential properties of monolayer HfX 2 (X = S, Se, or Te) are fully explored by first-principles calculations. The optimal lattice symmetries, sublattice buckling, electronic energy spectra, and density of states are systematically investigated. Monolayer HfS 2 , HfSe 2, and HfTe 2, respectively, belong to middle-gap semiconductor, narrow-gap one and semimetal, with various energy dispersions. Moreover, the van Hove singularities (vHs) mainly arise from the band-edge states, and their special structures in the density of states strongly depend on their two or three-dimensional structures and the critical points in the energy-wave-vector space. The above-mentioned theoretical predictions are attributed to the multi-orbital hybridizations of [ dx2−y2 , d xy , d yz , d zx , dz2 ]–[s, p x , p y , p z ] in the Hf-X chemical bonds. The diversified physical phenomena clearly indicate a high potential for applications, as observed in MoS 2 -related emergent materials ions.