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The dust extinction of gamma-ray bursts (GRBs) host galaxies, containingimportant clues to the nature of GRB progenitors and crucial for dereddening,is still poorly known. Here we propose a straightforward method to determinethe extinction of GRB host galaxies by comparing the observed optical spectrato the intrinsic ones extrapolated from the X-ray spectra. The rationale forthis method is from the standard fireball model: if the optical flux decayindex equals to that of the X-ray flux, then there is no break frequencybetween the optical and X-ray bands, therefore we can derive the intrinsicoptical flux from the X-ray spectra. We apply this method to three GRBs ofwhich the optical and X-ray fluxes have the same decay indices and another onewith inferred cooling break frequency, and obtain the rest-frame extinctioncurves of their host galaxies. The derived extinction curves are gray and donot resemble any extinction curves of local galaxies (e.g. the Milk Way, theSmall/Large Magellanic Clouds, or nearby starburst galaxies). The amount ofextinction is rather large (with visual extinction $A_V$ $\sim$1.6--3.4$\magni$). We model the derived extinction curves in terms of thesilicate-graphite interstellar grain model. As expected from the ``gray''nature of the derived extinction curve, the dust size distribution is skewed tolarge grains. We determine, for the first time, the local dust-to-gas ratios ofGRB host galaxies using the model-derived dust parameters and the hydrogencolumn densities determined from X-ray absorptions.

Determining the Dust Extinction of Gamma-ray Burst Host Galaxies: A Direct Method Based on Optical and X-ray Photometry