A majority of News Corp shareholders have voted against separating the roles of chairman and chief executive, both currently held by Rupert Murdoch.
Mr Murdoch's family owns about 12% of News Corp but, because of the dual class shareholding structure, has 40% of the voting shares in the company.
Two-thirds of votes cast, excluding the Murdoch family, wanted to separate the roles and have an independent chairman.
A resolution to change the shareholding structure was also rejected.
"There are plenty of media stocks to buy if they don't like this one," Mr Murdoch told the meeting.
"When you buy the stock, you know what the company is. If you don't like it, don't buy the stock."
Julie Tanner of the socially responsible Christian Brothers Investment Services proposed the resolution calling for an independent chairman.
"While Mr Murdoch claims that the interests of his family are in line with those of all shareholders, this vote proves that most independent shareholders would disagree," she said.
There was also support from about two-thirds of non-Murdoch votes for eliminating the distinction between voting and non-voting shares.
Corporate governance issues were raised after the phone-hacking scandal at News Corp's newspapers emerged last year.
"The failure of internal controls has had real and lasting repercussions," Julie Tanner said.
"It has shuttered a newspaper, launched criminal investigations, cancelled the BSkyB acquisition, eroded public trust and tarnished the company's reputation."
"This has been a difficult period in our company's 58-year history," Mr Murdoch told shareholders at the meeting in Los Angeles.
"We've acknowledged the serious wrongdoing that occurred in the United Kingdom," he said, adding that the company had "seized the opportunity to make amends" and to improve corporate compliance.
He said that the problems at its UK newspapers were not found in News Corp's other divisions.
Mr Murdoch also pointed out that News Corp's shares had risen 45% in the last 12 months.
News Corp has previously announced plans to split into two companies, separating its broadcasting and publishing businesses, with Mr Murdoch to chair both groups.
He told the meeting that the split would take time, and that there would be details on the executive leadership and board membership by the end of the year.