The structural stability and electronic structures of Nb planar atomic sheets are studied by employing first-principles plane wave pseudopotential method based on the density functional theory. The calculations for all the 2-dimensional lattice structures show that, as a result of Jahn-Teller effect, the high-symmetry square and hexagonal two-dimensional structures are metastable. The most stable structures are the low-symmetry oblique and centered rectangular structures, which are the distorted structures of the hexagonal 2-D structure due to Jahn-Teller effect. The 2-D rectangular structure of Nb atomic sheet can not be formed. The relative structural stabilities, the electronic energy bands and the density of states are discussed based on the ab initio calculations and the Jahn-Teller effect.