Cross sections of the 186W, 187Re, 188Os(γ,n) reactions were measured using quasi monochromatic γ-ray beams from laser Compton scattering (LCS), and results for the latter reaction are presented here. Neutron capture cross sections of the inverse reactions were evaluated by the Hauser-Feshbach statistical calculation where the experimental data were used to constrain the model parameters, especially the E1 strength function. The influence of the neutron capture by the 9.75 keV first excited state in 187Os which is substantially populated in stellar plasmas at typical s-process temperatures is examined in connection with the 187Re-187Os cosmochronology.