The isostructural and isoelectronic transition-metal-dichalcogenides 1T-TaS₂ and 1T-TaSe₂ are layered materials with intricate electronic structures. Combining the molecular beam epitaxy growth, scanning tunneling microscopy measurements and first-principles calculations, we prepare monolayer 1T-TaS₂ and TaSe₂ and explore their electronic structures at the atomic scale. Both two-dimensional (2D) compounds exhibit commensurate charge density wave phase at low temperature. The conductance mapping identifies the contributions from different Ta atoms to the local density of states with spatial and energy resolution. Both 1T-TaS₂ and 1T-TaSe₂ monolayer are shown to be insulators, while the former has a Mott gap and the latter is a regular band insulator.