We present the analysis of the binary-lens microlensing event OGLE-2013-BLG-0911. The best-fit solutions indicate the binary mass ratio of q 0.03, which differs from that reported in Shvartzvald et al. The event suffers from the well-known close/wide degeneracy, resulting in two groups of solutions for the projected separation normalized by the Einstein radius of s ~ 0.15 or s ~ 7. The finite source and the parallax observations allow us to measure the lens physical parameters. The lens system is an M dwarf orbited by a massive Jupiter companion at very close (M_(host) = 0.30^(+0.08)_(-0.06)M⊙, M_(comp) = 10.1^(+2.9)_(-2.2)M_(Jup), a_(exp) = 0.40^(+0.05)_(-0.04) au) or wide (M_(host) = 0.28^(+0.10)_(-0.08) M⊙, M_(comp) = 9.9^(+3.8)_(-3.5)M_(Jup), a(exp) = 18.0^(+3.8)_(3.5) au) separation. Although the mass ratio is slightly above the planet-brown dwarf (BD) mass-ratio boundary of q = 0.03, which is generally used, the median physical mass of the companion is slightly below the planet-BD mass boundary of 13M_(Jup). It is likely that the formation mechanisms for BDs and planets are different and the objects near the boundaries could have been formed by either mechanism. It is important to probe the distribution of such companions with masses of ~13M_(Jup) in order to statistically constrain the formation theories for both BDs and massive planets. In particular, the microlensing method is able to probe the distribution around low-mass M dwarfs and even BDs, which is challenging for other exoplanet detection methods