The Saturday night auction was part of the Dallas Safari Club's annual convention, KTVT-TV, Dallas/Fort Worth reported.
Namibia issues five permits a year to hunt the black rhino and the Dallas Safari Club said the permit it auctioned was possibly the first one ever sold in the United States.
More than 1,000 people preregistered to attend the event for the opportunity to bid on the permit.
The club said the goal was to raise $1 million from the sale of the permit, however, the winning bid of the auction was $350,000.
Namibia, which has an estimated black rhino population of just under 2,000, allows the selective hunting of older, post-breeding bulls that often attack younger bulls that are still breeding.
The TV news said scientists say there are only 4,000 wild black rhino, but the Safari Club issued a news release saying hunts have helped expand the rhino population.
"With hunting as part of its conservation program, Namibia's rhino population is growing as much as 5 percent annually," the group said.
The Dallas auction also drew dozens of protesters, KTVT reported.
"If people are really interested in conservation and keeping [rhinos] alive, why don't they use their money, their wealth in more productive ways other than killing a rhino. It doesn't make sense," protester Patti Weston, who drove from Louisiana to Dallas, told the TV station.