We report the discovery by the HATSouth network of HATS-7b , a transiting Super-Neptune with a mass of 0.120 \pm 0.012 M _ { J } , a radius of 0.563 _ { -0.034 } ^ { +0.046 } R _ { J } , and an orbital period of 3.1853 days . The host star is a moderately bright ( V = 13.340 \pm 0.010 mag , K _ { S } = 10.976 \pm 0.026 mag ) K dwarf star with a mass of 0.849 \pm 0.027 M _ { \sun } , a radius of 0.815 _ { -0.035 } ^ { +0.049 } R _ { \sun } , and a metallicity of [ Fe / H ] = +0.250 \pm 0.080 . The star is photometrically quiet to within the precision of the HATSouth measurements and has low RV jitter . HATS-7b is the second smallest radius planet discovered by a wide-field ground-based transit survey , and one of only a handful of Neptune-size planets with mass and radius determined to 10 % precision . Theoretical modeling of HATS-7b yields a hydrogen-helium fraction of 18 \pm 4 % ( rock-iron core and H _ { 2 } -He envelope ) , or 9 \pm 4 % ( ice core and H _ { 2 } -He envelope ) , i.e . it has a composition broadly similar to that of Uranus and Neptune , and very different from that of Saturn , which has 75 % of its mass in H _ { 2 } -He . Based on a sample of transiting exoplanets with accurately ( < 20 % ) determined parameters , we establish approximate power-law relations for the envelopes of the mass–density distribution of exoplanets . HATS-7b , which , together with the recently discovered HATS-8b , is one of the first two transiting super-Neptunes discovered in the Southern sky , is a prime target for additional follow-up observations with Southern hemisphere facilities to characterize the atmospheres of Super-Neptunes ( which we define as objects with mass greater than that of Neptune , and smaller than halfway between that of Neptune and Saturn , i.e . 0.054 M _ { J } < M _ { p } < 0.18 M _ { J } ) .