The one-tonne rover finished close-up investigation of a target sedimentary outcrop called "Shaler" last week. On July 4, it drove 18 meters away from Shaler.
On July 7, a second drive added another 40 meters on the trip toward a destination about 8 kilometres away, the entry to the lower layers of Mount Sharp.
"Mount Sharp, in the middle of Gale Crater, exposes many layers where scientists anticipate finding evidence about how the ancient Martian environment changed and evolved," NASA officials said in a statement.
In the Glenelg area, where Curiosity worked for the first half of 2013, the rover found evidence for an ancient wet environment that had conditions favourable for microbial life.
This means the mission already accomplished its main science objective, the US space agency said.