We present grids of limb-darkening coefficients computed from non-LTE, line-blanketed TLUSTY model atmospheres, covering effective-temperature and surface-gravity ranges of 15-55kK and 4.75dex (cgs) down to the effective Eddington limit, at 2x, 1x, 0.5x (Large Magellanic Cloud), 0.2x (Small Magellanic Cloud), and 0.1x solar. Results are given for the Bessell UBVRI_C_JKHL, Sloan ugriz, Stromgren ubvy, WFCAM ZYJHK , Hipparcos, Kepler, and Tycho passbands, in each case characterized by several different limb-darkening 'laws'. We examine the sensitivity of limb darkening to temperature, gravity, metallicity, microturbulent velocity, and wavelength, and make a comparison with LTE models. The dependence on metallicity is very weak, but limb darkening is a moderately strong function of logg in this temperature regime.