Photoneutron cross sections were measured for 58Ni, 60Ni, 61Ni, and 64Ni at energies between the one-neutron and two-neutron thresholds using quasimonochromatic γ -ray beams produced in laser Compton scattering at the NewSUBARU synchrotron radiation facility. These photoneutron data are used to extract the γ -ray strength function above the neutron threshold, complementing the information obtained by the Oslo method below the threshold. We discuss radiative neutron-capture cross sections and the Maxwellian-averaged cross sections for Ni isotopes including 63Ni, a branching point nucleus along the weak s-process path. The cross sections are calculated with the experimentally constrained γ -ray strength functions from the Hartree-Fock-Bogolyubov plus quasiparticle–random-phase approximation based on the Gogny D1M interaction for both E1 and M1 components and supplemented with the M1 upbend.