The neutron capture cross section of the unstable s-process branching nucleus W-185 has been derived from experimental data of the inverse W-186(gamma,n)W-185 photodisintegration taken with monochromatic photon beams from laser Compton scattering. The result of sigma=553+/-60 mb at kT=30 keV leads to a relatively high effective neutron density in the classical s process of N-n=4.7x10(8) cm(-3). A realistic model for the s process in thermally pulsing asymptotic giant branch stars overestimates the abundance of Os-186 significantly because of the relatively small neutron capture cross section of W-185.