Haitian authorities have urged people in the poor Caribbean nation to take precautions amid fears of landslides and widespread flooding.
Haiti, hit a week ago by a tropical storm that left more than two dozen dead, is vulnerable to mudslides because of widespread deforestation.
The storm is expected to bring rainfall of 64cm (25 inches) in some areas.
Gustav has grown more powerful since it strengthened to a category one hurricane earlier on Tuesday.
Haitian Interior Minister Paul-Antoine has appealed for international bodies to help his government cope with the storm's aftermath.
'Flash floods and mud slides'
At 1800 GMT, Gustav's centre was located some 60 kms (40 miles) southwest of the Haitian capital, Port-au-Prince.
Gustav's heavy rainfall "will likely produce life-threatening flash floods and mud slides," said the Miami-based National Hurricane Center (NHC).
It was moving in a north-western direction at 16 km/h and was expected to head towards Cuba early on Wednesday, the NHC said.
Haiti is still recovering from the last storm, Fay, which swept across the Caribbean and the south-eastern US last week.
Neighbouring Dominican Republic, which shares the island of Hispaniola with Haiti, has issued a hurricane warning for the south-west of the country.
The Cuban authorities have also issued a hurricane watch for the provinces of Las Tunas, Granma, Holguin, Santiago de Cuba and Guantanamo.
Gustav is the seventh tropical storm of the Atlantic hurricane season
vulnerable 易受傷的, 易受責難的;有弱點的;難防守的
appealed for 呼籲,懇求