Dislocations are line defects and the primary carriers of plastic deformation in crystals. We derive a Green’s function formulation for the climb motion of curved dislocations and multiple dislocations in three-dimensions. In this new dislocation climb formulation, the dislocation climb velocity is determined from the Peach-Koehler force on dislocations through vacancy diffusion in a non-local manner. We also present a numerical discretization method of this Green’s function formulation appropriate for implementation in discrete dislocation dynamics simulations.