  We report on the first detection of X-ray dust scattered rings from the
Galactic low mass X-ray binary V404 Cyg. The observation of the system with
Swift/XRT on June 30 2015 revealed the presence of five concentric ring-like
structures centred at the position of V404 Cyg. Follow-up Swift/XRT
observations allowed a time-dependent study of the X-ray rings. Assuming that
these are the result of small-angle, single X-ray scattering by dust grains
along the line of sight, we find that their angular size scales as $\theta
\propto\sqrt{t}$ in agreement with theoretical predictions. The dust grains are
concentrated in five dust layers located at about 2.12, 2.05, 1.63, 1.50 and
1.18 kpc from the observer. These coincide roughly with locations of enhanced
extinction as determined by infrared photometry. Assuming that the grain size
distribution is described by a generalized Mathis-Rumpl-Nordsieck model, we
find that the power-law index of the most distant cloud is $q\sim 4.4$, while
$q \sim 3.5-3.7$ in all other clouds. We constrain at a $3\sigma$ level the
maximum grain size of the intermediate dust layers in the range
$0.16-0.20\,\mu$m and set a lower limit of $\sim 0.2\,\mu$m in the other
clouds. Hints of an exponential cutoff at the angular intensity profile of the
outermost X-ray ring suggest that the smallest grains have sizes $0.01 \mu{\rm
m}\le \alpha_{\min} \lesssim 0.03\,\mu$m. Based on the relative ratios of dust
column densities we find the highest dust concentration at $\sim 1.6$ kpc. Our
results indicate a gradient in the dust properties within 1 kpc from V404 Cyg.
