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 : m _ { b } sin i = 11.1 ^ { +0.4 } _ { -1.1 } M _ { \tiny jup } , a = 4.9 ^ { +0.14 } _ { -0.13 } AU and e = 0.59 ^ { +0.05 } _ { -0.02 } . Considering random inclination angles , this object has \gtrsim 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 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 \sim 2 deg . This value corresponds to an upper mass limit of \sim 0.3 M _ { \odot } , therefore the probability that HIP 67537 b is stellar in nature is \lesssim 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 EXPRESS radial velocity program , which corresponds to a detection fraction of f = 1.6 ^ { +2.0 } _ { -0.5 } % . 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 .