V404 Cyg is a nearby (d = 2.39 ±0.14 kpc) low mass X-ray binary that exhibited a re-brightening on June 15 2015 after a long period of quiescence (26 yr). The observation of the system with Swift/XRT on June 30 2015 revealed the presence of five concentric ring-like structures centered at the position of V404 cyg; this is the first detection of X-ray dust scattered rings from the Galactic low mass X-ray binary V404 cyg. Follow-up Swift/XRT observations allowed a time-dependent study of the X-ray rings, whose angular size scales as θ∝√t, in agreement with theoretical predictions of small-angle, single X-ray scattering by dust grains along the line of sight. We showed that 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 power-law model, we were able to determine the power-law index (3.5-3.7 ≤ q ≤ 4.4) and set constrains on the maximum (0.16-0.20 μm) size of the grains. Based on the relative ratios of dust column densities we found the highest dust concentration at ~1.6 kpc. In brief, our results indicated a gradient in the dust properties within 1 kpc from V404 cyg.