Depending on which islands you mean. There are the U.S.(North America) Virgin Islands. Or there's the British Virgin Islands.
The US Virgin Island belong to the continent of North America.
Great Britain
Islands in an ocean don't belong to any continent. If they were part of a continent they wouldn't be islands would they? The African Continent is the continent nearest the Canary Islands, but the islands are the result of volcanic activity on the ocean floor.
Asian continent
The islands that are belonging to the United Kingdom are: England, Pitcairin Islands, Falkland Islands, Montserrat, Saint Helena, Cook Islands, British Virgin Islands, Turks and Caicos Islands, and Cayman Islands.
The Cayman Islands do not belong to any city. They are a British territory.
South America
They are often referred to as Oceania.
Lanzarote is the 4th largest island in the Canary Islands. It is volcanic in origin and about 125 kilometres from the nearest continent. It does not "belong" to any continent.
Puerto Rico and the US Virgin Islands
Never.There is no such official geographic or state entity as the U.S. Virgin Islands. The correct legal name is "Virgin Islands" and were so name by Christopher Columbus in 1493 on his second voyage to the "New World" in honor of St. Ursula and her 11,000 martyred virgin handmaidens."U.S. Virgin Islands" is simply a nick-name with no legal status that is used to let people know that the Islands belong to the United States and are not the British Virgin Islands.Noteworthy Fact: Salt River on St. Croix, Virgin Islands, is the only place in United States of America that Columbus visited.
British Columbia owns all the islands off its coast, the islands off the Alaskan coast belong to Alaska. The Queen Charlotte Islands, Dundas Island, Stephens Island and the islands below belong to British Columbia. Anything above Dundas Island is part of Alaska.
The Cayman Islands are considered a British Overseas Territory. The Islands are one of 14 British Territories that have voted to remain territories of Britain.