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We study the relaxation of perturbed low-angle tilt grain boundaries by climb of the constituent dislocations. Under the combined influence of the long-range effects due the Peach–Koehler force and vacancy diffusion, dislocation climb always stabilizes the grain boundaries on a time scale that is proportional to the square of the perturbation length scale and inversely proportional to the point defect diffusivity. This relaxation has a different nature from that of perturbed low-angle grain boundaries by dislocation glide, in which only the long-range Peach–Koehler force is important, leading to a perturbation relaxation time linearly proportional to the perturbation wavelength itself.