Gjesvær (Northern Sami: Geaissvearra) is an old fishing village in Nordkapp Municipality in Finnmark county, Norway. It is the only place in Finnmark known from the Viking Age and is mentioned in the Heimskringla saga as Geirsver. The name comes from the man's name Geir, which means "spear".
The location was used by Vikings on the way to Bjarmaland (see Ottar from Hålogaland), and probably also for gathering food on the nearby Gjesværstappan islands which contain one of the largest seabird colonies in Norway.
Like most other places in Finnmark, all buildings in the village were burned down in 1944 by the German occupying forces. Gjesvær Chapel, built in 1960, is considered a cultural monument.
Gjesvær has approximately 130 inhabitants, but at the beginning of the 1970s, it had about 350 people. It has a fish plant, local shop, post office, and primary school. The main industry is fishing, but in recent years there has been an increased emphasis on tourism, activities including fishing and bird watching trips to the Gjesværstappan nature reserve.