We report the discovery and the analysis of the short timescale binary-lens microlensing event , MOA-2015-BLG-337 . The lens system could be a planetary system with a very low mass host , around the brown dwarf/planetary mass boundary , or a brown dwarf binary . We found two competing models that explain the observed light curves with companion/host mass ratios of q \sim 0.01 and \sim 0.17 , respectively . A significant finite source effect in the best-fit planetary model ( q \sim 0.01 ) reveals a small angular Einstein radius of \theta _ { E } \simeq 0.03 mas which favors a low mass lens . We obtain the posterior probability distribution of the lens properties from a Bayesian analysis . The results for the planetary models strongly depend on a power-law index in planetary mass regime , \alpha _ { pl } , in the assumed mass function . In summary , there are two solutions of the lens system : ( 1 ) a brown dwarf/planetary mass boundary object orbited by a super-Neptune ( the planetary model with \alpha _ { pl } = 0.49 ) and ( 2 ) a brown dwarf binary ( the binary model ) . If the planetary models are correct , this system can be one of a new class of planetary system , having a low host mass and also a planetary mass ratio ( q < 0.03 ) between the companion and its host . The discovery of the event is important for the study of planetary formation in very low mass objects . In addition , it is important to consider all viable solutions in these kinds of ambiguous events in order for the future comprehensive statistical analyses of planetary/binary microlensing events .