The National Sleep Foundation telephone poll of more than 1,000 people from the four ethnic groups also showed that more black Americans are likely to do job related work before bed.
Black Americans have long suffered from higher jobless rates than white Americans, a phenomenon that in recent years spread to Hispanics.
So many people are suffering because of economic uncertainty, said Martica Hall, associate professor of psychiatry at the University of Pittsburgh.
If you find yourself lying awake worrying, write a note to yourself to work on these issues the next day, she said.
Black Americans are also more likely to pray and have sex before going to bed and need the least amount of sleep to function, the survey found.
The hour before bed is an important time to relax and wind-down before going to sleep, says Thomas Balkin, chairman of the National Sleep Foundation.
For those who are having problems sleeping, it's a good idea to consider whether your bedtime routines may be too alerting, he said.
Asians report getting the best sleep, having the least amount of sleep problems and the most infrequent use of sleep aids, the poll showed, while whites are more likely to sleep with their pet or partner.
Three quarters of each group associated poor sleep with health problems, while one fifth reported missing events at least one day in the past month because they were too sleepy or had a sleep problem.
One in five from each group said sleepiness had affected their relationships.
Whites and Asians were more likely than blacks and Hispanics to blame a lack of sleep for harming their job performance, hindering their ability to carry out household duties and care for their family.