Using first principles calculations, we investigate the structural, vibrational and electronic structures of the monolayer graphene-like transition-metal dichalcogenide (MX 2) sheets. We find the lattice parameters and stabilities of the MX 2 sheets are mainly determined by the chalcogen atoms, while the electronic properties depend on the metal atoms. The NbS 2 and TaS 2 sheets have comparable energetic stabilities to the synthesized MoS 2 and WS 2 ones. The molybdenum and tungsten dichalcogenide (MoX 2 and WX 2) sheets have similar lattice parameters, vibrational modes, and electronic structures. These analogies also exist between the niobium and tantalum dichalcogenide (NbX 2 and TaX 2) sheets. However, the NbX 2 and TaX 2 sheets are metals, while the MoX 2 and WX 2 ones are semiconductors with direct-band gaps. When the Nb and Ta atoms are doped into the MoS 2 and WS 2 sheets, a semiconductor-to-metal transition occurs. Comparing to the bulk compounds, these monolayer sheets have similar structural parameters and properties, but their vibrational and electronic properties are varied and have special characteristics. Our results suggest that the graphene-like MX 2 sheets have potential applications in nano-electronics and nano-devices.