  Using photometric and spectroscopic data of Supernova (SN) 2012cu, a fairly
reddened type Ia supernova, we derived its color excess curves and probed the
dust extinction in its host galaxy, NGC 4772. In order to derive the extinction
as a function of wavelength (i.e., $A_\lambda$), we model the color excess
curves of SN 2012cu in terms of dust models consisting of silicate and
carbonaceous (graphite or amorphous carbon) dust. The modeled extinction law
towards SN 2012cu extends flatly to the far-ultraviolet (UV) bands, which is
much flatter than those of the Milky Way and Magellanic Clouds, and the 2175
$\AA$ feature is very weak or absent. The flatness of the modeled extinction
curve in the UV bands suggests a "grey" extinction law of the active galactic
nucleus in the vicinity of the SN 2012cu-Earth line of sight. Our results
indicate that the sizes of the dust in the ISM towards SN 2012cu in NGC 4772
are larger than those of the Milky Way and the Large Magellanic Cloud, and much
larger than that of the Small Magellanic Cloud. The best fitting gives an
observed visual extinction towards SN 2012cu of $A_V \approx 2.6$ mag, a
reddening of $E(B-V) \approx 1.0$ mag, with a total-to-selective extinction
ratio $R_V \approx 2.7$, consistent with previous results.
