In this paper, investigation of the structure of palladium nanowire has been performed by using genetic algorithm simulation based on the molecular dynamics. Our calculation employs a well-fitted, tight-binding many-body potential for Pd atoms. Some local atomic structures and defects in nanowires have been reported. The melting behavior of palladium nanowire has also been investigated. An interesting result is that the diffusion of the central atoms results in the beginning of the melting. The moving central atoms build up a monostrand atomic chain during the melting process. The single atomic chain is very stable which can exist in a wide temperature region (800-950 K). The formation of the single atomic chain causes some new defects in the nanowire. And the new defects result in the decrease of the thermal stability of the nanowire. Interestingly, the liquid from the nanowire melting has a supercooled feature because the splitting of the second peak of pair correlation function is observed. The curves of the internal energy and the local cluster are used to monitor the phase transition. The melting of the nanowire is not only due to the single atomic diffusion, but also the diffusion of the local clusters.