The Virgin Islands are two countries, US Vigin Islands and the British Virgin Islands.
The US islands have the same entry requirements as the USA
The British Islands require visas from people from;
Afghanistan, Albania, Algeria, Angola, Armenia, Azerbaijan, Bahrain, Belarus, Benin, Bhutan, Bosnia-Herzegovina, Burkina Faso, Burundi, Burma, Cambodia, Cameroon, Cape Verde, Central African Republic, Chad, China (except Hong Kong SAR), Columbia, Comoros, Congo (Democratic Republic), Cuba, Djibouti, Dominican Republic, Egypt, Equatorial Guinea, Eritrea, Ethiopia, Gabon, Georgia, Guinea, Guinea-Bissau, Guyana, Haiti, Indonesia, Iran, Iraq, Israel, Ivory Coast, Jamaica, Jordan, Kazakhstan, Kirghistan, Korea (North), Kuwait, Laos, Lebanon, Liberia, Libya, Macedonia, Madagascar, Mali, Mauritania, Moldova, Mongolia, Montenegro, Morocco, Myanmar, Nepal, Niger, Nigeria, Oman, Pakistan, Occupied Palestinian Territories, Peru, Philippines, Qatar, Russian Republic, Rwanda, Sao Tome & Principle, Saudi Arabia, Senegal, Serbia, Somalia, Sudan, Suriname, Syria, Taiwan, Tajikistan, Thailand, Togo, Turkish Republic of Northern Cyrus, Turkmenistan, Ukraine, United Arab Emirates, Uzbekistan, Vietnam and Yemen.
Everyone else can stay for up to 30 days without a visa.
Holders of a valid visa or residency from Canada, United Kingdon or USA with more than six(6) months of validity remaining can enter without a visa.
British Virgin Islands visa information