The first generation Supra was based largely upon the Toyota Celica liftback, but was longer by 5.1 in (129.5 mm). The doors and rear section stayed the same length as Celica but rear panels differed. The most important change was the swap to an Inline-6 instead of the stock Celica's 4-cylinder engine. Toyota's original plan for the Supra at this time was to make it a competitor to the very popular Datsun (now Nissan) Z-car.

1979

In 1978 Toyota began production of the Mark I Supra in Japan, as the Toyota Celica XX. The year it debuted in the United States and Japan was in 1979. The USA Mark I (chassis code MA46) was originally equipped with a 110 hp (82 kW) 2.6 L (2563 cc) 12-valve SOHC inline-6 engine (4M-E). Simultaneously in 1979, the Japanese Mark I (chassis code MA45) was offered with a 110 hp (82 kW) 2.0 L 12-valve SOHC inline-6 engine (M-EU). Both were the first Toyota engines equipped with electronic fuel injection.
 
Drivetrain options for the Mark I were either a 5-speed manual (W50) or an optional 4-speed automatic transmission (A40D). Both transmissions featured an overdrive gear. The top gear in the 5-speed was its overdrive gear whereas the automatic transmission featured an overdrive gear that would engage at speeds over 35 mph. The drivetrain for the Supra retained the T series solid rear axle configuration of the Celica in the Japanese MA45 version and a larger F series (and optional Limited Slip Differential) in the MA46 and MA47. The car also came standard with 4-wheel disc brakes and featured a four-link rear suspension with coil springs, lateral track bar, and stabilizer bar. The front suspension consisted of MacPherson struts and a stabilizer bar.

On the inside of the Supra one had an option of power windows and power locks as part of the convenience package. The convenience package also included cruise control and special door trim with door pull straps, with an optional sunroof. As for standard features, in the center console there was an extendable map light and a fliptop armrest, which provided storage. Some other features were the tilt steering wheel, deep zippered pockets on the backs of the front seats, and tonneau cover under the liftback. The dashboard also contained a state-of-the-art (at the time) AM/FM/MPX 4-speaker stereo radio, analog clock, and tachometer as part of the instrument panel.

1980

In 1980, the Japanese Mark I (also branded with the MA46 chassis code) was offered with a 145 hp (108 kW) 2.0 L (1988 cc) 12-valve SOHC Turbocharged inline-6 engine (M-TEU). The engine was equipped with a Garrett T03 Turbo, but was not intercooled. This was the first Toyota engine to utilize a turbocharger.
 
The changes for the 1980 US version were different, but mostly cosmetic. The interior received a redesigned center console and a digital quartz clock. On the exterior were redesigned side view mirrors, the 14x5.5 aluminum rims, which were optional in 1979, are now standard (the 1979s had steel rims with plastic wheel covers standard). In addition body molded mudflaps became available. On the copper metallic and white cars the mudflaps were painted the body color while the mudflaps were left black on all other colors. On the rear of the mudflaps, the word "Celica" was painted in white lettering.
 
The official Toyota Supra Site also notes that there was an addition of optional leather-trimmed seating and automatic climate-control.

1981

In the coming year, 1981, the Supra received an upgrade in displacement with the 2.8 L (2759 cc) 5M-E engine. It is still a 12-valve SOHC engine, but makes 116 hp (87 kW) and 145 ft•lbf (197 N•m) of torque. The cars automatic transmission was changed to the revised Toyota A43D and it gained a revised final drive gearing. Because of the change in engine and transmission they dubbed a new chassis code of MA47. The final year of the MK I Supra it achieved a 0-60 mph time of 10.24 seconds and finished the 1/4 mile in 17.5 seconds at 77.7 mph.
 
Also in 1981, a new Sports Performance Package became an option, which included sport suspension, raised white letter tires, and front and rear spoilers. This also marked the last year that the 8-track cartridge was offered in any Supras.