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Monolayer NbSe₂ has recently been shown to be a two-dimensional superconductor, with a competing charge-density wave (CDW) order. This work investigates the electronic structure of monolayer NbSe₂ based on first-principles calculations, focusing on charge and magnetic orders. It is found that decreased screening in the monolayer NbSe₂ with a perfect lattice exhibits magnetic instability, which is removed by the formation of CDW. Two energetically competitive but distinct 3 × 3 CDW structures are revealed computationally, which have a significant impact on the Fermi surface. The relations of the potential CDW phases with experimental structure and the coexisting superconductivity are discussed.