The geometric and electronic structures of Molybdenum chains are studied by the first-principles of density-functional method. The present calculations reveal that Molybdenum can form planner chains in zigzag, dimer, and ladder structures. The most stable geometry is the Dimer structure chain. The ladder structure is found to be more stable than the zigzag one. Furthermore, the relative structural stability, the electronic energy bands, the density of states are discussed based on the ab initio calculations.