In the autumn of 2001, the third development version of the JD 6000 series, the 6020 series, was introduced. Thanks to the new design of the engine hood, the appearance differed significantly from the 6010 series. The nominal power ratings of the 4-cylinder models remained unchanged, except for the 6420, but the torque values had improved slightly. The highest power, however, was achieved below 200 rpm from the nominal speed. The new model in the lineup was the 6420 S, where the nominal power increased from 110 to 120 hp when power was transmitted via the power take-off (PTO) or when the speed exceeded 15 km/h. The engine oil change interval was extended to 500 hours when using JD oils.

Premium-equipped versions featured the familiar 24+24 transmission, which included a 4-speed hydraulic power shift. From the 6320 model onwards, a 50 km/h transmission was also available. The basic transmission was known as PowerQuad Plus. It had an electrically hydraulic directional shuttle lever on the left side of the steering wheel. The power shift buttons were located on the gear lever knobs, and an additional rocker switch was available on the side panel. When changing the range gear, the power shift automatically switched to the most suitable gear. An optional feature was AutoQuad 2, where the automation selected the optimal power shift based on engine speed and load. Two driving programs could be chosen, and the automation could be overridden with buttons.

At the end of 2003, AutoQuad 2 was replaced by AutoQuad Plus, which softened the engagement of power shifts by adjusting the engine speed during shifting. A different power shift gear could be preselected for reverse compared to forward driving. The shift speed of the power shift could be adjusted up to 340 rpm. An optional EcoShift transmission was available, where the gear ratios were the same as in the 50 km/h version: in the 40 km/h version, the top speed was electronically limited and reached at 1700-1900 rpm.

The Premium Plus versions of the 6320 and 6420 models featured a continuous variable transmission, which is described in more detail in the presentation of the larger models. Premium Plus models also included electrically operated hydraulic valves and a control armrest.

Lifting capacity was slightly increased compared to earlier models. The lift system was equipped with a suspension that softened the ride during transport. The range of optional equipment was more extensive than before. The cab was lightly updated. Noise level was initially 75 dB and from 2003 onwards 73 dB.

Starting from 2003, the 6320 and 6420 models had engines based on four-valve technology and Denso Common Rail injection, where the best torque was achieved over a wider rpm range than before. During 2003, the front axles were also changed from ZF to Dana.

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