Tungsten-188 (t(1/2) = 69.4 d) is routinely produced by double neutron capture using highly enriched W-186 target, W-186(n,gamma)W-187(n,gamma)W-188 reaction, at the ORNL 85 MWt High Flux Isotope Reactor. While the thermal neutron cross section for the first reaction, W-186(n,gamma)W-187, is well known, the single reported 64 b cross-section for the second reaction, W-187(n,gamma)W-188, cannot be validated by experimental results that yield lower than expected activities of W-188. In this study, we report a new value for the thermal neutron capture cross section of W-187. After confirming the neutron capture cross section of W-186 (sigma(0) = 37.8 +/- 1.8 b for thermal and I-0 = 476 +/- 25 b for resonance integrals with sigma(0)/I-0 = 12.6 +/- 0.4) in two short irradiations, longer irradiations (1-10 d) were performed to obtain a value of 6.5 +/- 0.8 b for the sigma(0) of W-187, which is lower than the adopted value by a factor of 10. Due to the short half-life of W-187 (t(1/2) = 23.7 d), the sigma(0) for W-187 was obtained empirically by comparing the W-188 experimental yields with the theoretical yields generated by code IsoChain and varying the W-187 cross section while keeping all other parameters constant.