Unfortunately no, according to Wikitravel.
There is no road or rail system. The easiest way to get around
Greenland is by plane, particularly Air Greenland. In the summer,
Arctic Umiaq Line passenger ships provide service to destinations
between Narsarsuaq and Uummannaq along the west coast.
Of course, if you got a skidoo or dog sled, you could make your own way around ;)
Wikipedia actually has more information - Transport in Greenland
The transportation system in Greenland is very unusual in that
Greenland has no railways, no inland waterways, and virtually no roads
It goes into further detail about the few roads that do exist:
There are 150 km (90 mi) of roads in the whole country; 60 km (40 mi)
of the roads are paved. Two towns are connected by a 4.5 km road,
Ivittuut and Kangilinnguit; the rest are isolated.