It is the current local time right now in Saint Croix, Charlotte Amalie, Cruz Bay and in all United States Virgin Islands’ cities. 
United States Virgin Islands’ time zone: AST or UTC-04:00

No daylight saving time (DST) in United States Virgin Islands.

Full name: United States Virgin Islands
Continent: North America
Region: Caribbean
Population: 108,708
Area: 352 km²
Capital: Charlotte Amalie
Currency: Dollar (USD)
Phone code: +1-340
Domain: .vi
Wikipedia article: United States Virgin Islands