We report the discovery of a substellar companion around the giant star HIP 67537. Based on precision radial velocity measurements from CHIRON and FEROS high-resolution spectroscopic data, we derived the following orbital elements for HIP 67537 b: mb sin i = 11.1+0.4 -1.1+0.4-1.1Mjup, a =4.9+0.14 -0.13a=4.9-0.13+0.14 AU and e = 0.59+0.05 -0.02 e=0.59-0.02+0.05. Considering random inclination angles, this object has ≳ 65% probability to be above the theoretical deuterium-burning limit, thus it is one of the few known objects in the planet to brown-dwarf (BD) transition region. In addition, we analyzed the Hipparcos astrometric data of this star, from which we derived a minimum inclination angle for the companion of ∼2 deg. This value corresponds to an upper mass limit of ∼ 0.3 M⊙, therefore the probability that HIP 67537 b is stellar in nature is ≲ 7%. The large mass of the host star and the high orbital eccentricity makes HIP 67537 b a very interesting and rare substellar object. This is the second candidate companion in the brown dwarf desert detected in the sample of intermediate-mass stars targeted by the EXoPlanets aRound Evolved StarS (EXPRESS) radial velocity program, which corresponds to a detection fraction of f = +2.0 -0.5 f=1.6-0.5+2.0%. This value is larger than the fraction observed in solar-type stars, providing new observational evidence of an enhanced formation efficiency of massive substellar companions in massive disks. Finally, we speculate about different formation channels for this object.