Fiat 1000 and 1300 were replaced at the end of 1979 by new Grandi models. The design was consistent with the smaller models. In terms of external dimensions, the Grandi were quite compact compared to modern-day tractors. The Pininfarina Cabina Larga cabin was larger than in the smaller models. The 1180 had a naturally aspirated 5.5-liter engine. The 1380 (135 hp) had the same engine but turbocharged; in between them was the turbocharged 1280, which was not brought to Finland. Of the 8.1-liter engines, the 1580 (155 hp) was naturally aspirated and the 1880 (180 hp) turbocharged. In 1982, the 1580 also received a turbocharger and 5 more horsepower.

The transmission in the Grandi was 12+4. In Finland, nearly exclusively the 24+8 version equipped with a creeper gear was sold. The gear levers were located on the dashboard. The power take-off clutch was hydraulic, differing from the smaller Fiats. The front-wheel drive power was delivered directly from the transmission via a central shaft. The turning circle diameter was as much as 13.2 meters even in the smaller models, and 14.6 meters in the 1580 and 1880. At the end of 1980, the front axle lock became standard; it was a hydraulically engaged dog lock, while the largest models had a disc lock. At the same time, the orange color was changed to a darker terracotta.

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