Pressure dependencies of electronic structures and lattice dynamics of Pd which is close to ferromagnetic instability at ambient pressure are investigated on the basis of first-principles calculations. Particular attention is paid to phonon-mediated superconductivity: the transition temperature T c without taking into account spin fluctuation effects are estimated to be 6.40–8.55 K at ambient pressure and 0.58–1.44 K at 50 GPa. Though spin fluctuation effects would suppress the superconducting transition at 0 GPa, under pressures the transition would appear due to the rapid decreasing of spin fluctuation effects with increasing pressure. We estimate the T c at 50 GPa to be at most 0.71 K if we include spin fluctuation effects.