The mechanical properties including elastic stiffness constants as well as bulk modulus of Palladium (Pd) nanowire were calculated in the constant temperature and pressure (NPT), ensemble by molecular dynamics (MD) simulation technique. The quantum Sutton-Chen (Q-SC) many-body potential was used to calculate the cohesive energy as well as forces experience by every atoms. The temperature and pressure of nanowire were controlled by Nose-Hoover thermostat and Berendsen barostat, respectively. The periodic boundary condition (PBC) was only applied along the axis of nanowire. The MD results show that the mechanical properties depend on diameter of nanowire. Our results show that elastic constants including C11 , C12 , C44 and bulk modulus increase nonlinearly with increasing the diameter of nanowire and then reach a constant value, which is a typical behavior of nanoscopic systems.