Cross sections of the 186 W, 187 Re, 188 Os(γ, n) reactions were measured using quasi-monochromatic photon beams from laser Compton scattering (LCS) with average energies from 7.3 to 10.9 MeV. The results are compared with the predictions of Hauser-Feshbach statistical calculations using four different sets of input parameters. In addition, the inverse neutron capture cross sections were evaluated by constraining the model parameters, especially the E1 strength function, on the basis of the experimental data. The present experiment helps to further constrain the correction factor Fσ for the neutron capture on the 9.75 keV state in 187 Os. Implications of Fσ to the Re-Os cosmochronology are discussed with a focus on the uncertainty in the estimate of the age of the Galaxy.PACS numbers: PACS number(s): 25.40.Lw,26.20.+f