Gylfi is a mythological Norse king. Other people with Gylfi as a given name include:
Gylfi Einarsson, Icelandic footballer Gylfi Gylfason, Icelandic handball player Gylfi Magnússon, Icelandic economist Gylfi Sigurðsson, Icelandic footballer Gylfi Zoega, Icelandic economist Gylfi Þorsteinsson Gíslason, Icelandic politician Sigurður Gylfi Magnússon, Icelandic historian