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, Burundi, Burma, Cambodia, Cameroon, Cape Verdi, 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.
British Virgin Islands visa information