The man also suffered from chronic health problems, health officials said.
Last week, health officials in Contra Costa County announced that a 9-year-old girl in that county who had tested positive for H1N1 died May 29.
Four swine flu-related deaths have been reported statewide.
Alameda County health officials are reminding residents to take precautions to prevent the spread of germs. However, there are no new school closures or event cancellations related to swine flu.
"So far in Alameda County, we have been seeing mostly mild cases of the H1N1 virus and in most cases people have been able to rest at home and the symptoms go away," Alameda County Public Health Department spokeswoman Sherri Willis said.
"This particular gentleman had a number of health issues and had been hospitalized, and the swine flu was one of the conditions he was being treated for," Willis said.
A vaccine for the virus does not yet exist, so health officials encourage residents to take steps to protect themselves.
"Even though flu season is over, we would like to remind people that spreading germs is something that they should be conscious about year-round," Willis said.
Residents are advised to wash their hands often with soap and water, using alcohol-based hand cleaners if soap and water are not available, and cover the nose and mouth when coughing or sneezing.
Those with symptoms are advised to avoid social gatherings, including work and school, so as to not infect others.
Health officials are continuing to investigate 48 confirmed and 10 probable cases of the H1N1 virus reported in Alameda County.