We report the discovery of a super-Earth mass planet in the microlensing event MOA-2012-BLG-505 . This event has the second shortest event timescale of t _ { E } = 10 \pm 1 days where the observed data show evidence of planetary companion . Our 15 minute high cadence survey observation schedule revealed the short subtle planetary signature . The system shows the well known close/wide degeneracy . The planet/host-star mass ratio is q = 2.1 \times 10 ^ { -4 } and the projected separation normalized by the Einstein radius is s = 1.1 or 0.9 for the wide and close solutions , respectively . We estimate the physical parameters of the system by using a Bayesian analysis and find that the lens consists of a super-Earth with a mass of 6.7 ^ { +10.7 } _ { -3.6 } M _ { \oplus } orbiting around a brown-dwarf or late M-dwarf host with a mass of 0.10 ^ { +0.16 } _ { -0.05 } M _ { \odot } with a projected star-planet separation of 0.9 ^ { +0.3 } _ { -0.2 } AU . The system is at a distance of 7.2 \pm 1.1 kpc , i.e. , it is likely to be in the Galactic bulge . The small angular Einstein radius ( \theta _ { E } = 0.12 \pm 0.02 mas ) and short event timescale are typical for a low-mass lens in the Galactic bulge . Such low-mass planetary systems in the Bulge are rare because the detection efficiency of planets in short microlensing events is relatively low . This discovery may suggest that such low mass planetary systems are abundant in the Bulge and currently on-going high cadence survey programs will detect more such events and may reveal an abundance of such planetary systems .