The car appears to be the #36, driven by Takuya Kurosawa and Masanori Sekiya, who achieved a 2nd place finish in the GT500 class of the 1999 JGTC season.
This description is taken from the NTSC version of Gran Turismo 2:
The All-Japan GT Championship began in 1993. The Supra GT has entered it every year since 1994, and in 1997, after growing faster with age, finally defeated arch rival Skyline GT-R to win the series championship.
The GT is based on showroom Supra models but has been modified to the full extent allowed by regulations. These many modifications are designed to achieve race-winning performance by bringing out the car's full potential.
Despite the body size, scrupulous weight reduction measures have shaved off every excess ounce to lower the vehicle's weight to an amazingly low 2,420 lbs, the minimum allowed.
In place of the showroom Supra's in-line 6-cylinder power unit, the Supra GT contains the same engine used by Celica in the WRC: the model 3S-GTE, a 1,998 cc DOHC in-line 4-cylinder engine positioned as far back as possible in the engine room and capable of generating a maximum output of 465 hp or more at 6,000 rpm and a maximum torque of 470 lb-ft or more at 4,500 rpm. A 43.9 mm air restrictor is installed to comply with output regulations. The transmission is a sequential 6-speed Hewland transmission with a triple-plate AP clutch. The chassis has the same double wishbone front and rear suspension as the standard model but also has longer arms and numerous Group C components, mounted to the steel chassis.
Alterations cover every aspect of the car's design. The driving position is further back than in the standard Supra for better weight distribution. This is the ultimate in modified cars.
This car can be purchased in the special section of the Toyota dealership for 1,000,000 Credits.