A New York bank and an Illinois pension fund submitted an amended complaint yesterday in Delaware Chancery Court.
They accuse the board of allowing News Corp chairman and chief executive Rupert Murdoch to misuse the company resources to gain political influence.
The filing says that News Corp directors knew that some of the company's reporters had hacked into mobile phones and bribed police officers in 2009.
But the board members refused to properly investigate the acts over fear of upsetting Murdoch and his children who serve as company executives, the suit alleges.
According to Bloomberg, the filing claims that the board's approach was a "textbook example of failed corporate governance and domination by a controlling shareholder".
It also accuses the directors of having "condoned Murdoch's use of News Corp to pursue his quest for power, control, and political gain" at shareholders' expense.
News Corp has not responded to the lawsuit.
But the company did issue a statement on Monday denying reports the James Murdoch, News Corp's deputy chief operating officer, may have obstructed the Leveson inquiry into media ethics.
The Inquiry was set up after the closure of the News of the World, which was scuttled following a string of revelations about voicemail interception by journalists.
Police are currently investigating whether James Murdoch may have failed to disclose an iPhone allegedly used by senior executives at the paper's publisher News International.
Rupert Murdoch told the Leveson Inquiry in April that there had been a "cover up" at the News of the World, but denied that he had been party to it.
But in its report on the hacking affair, the Commons culture, media and sport committee said that Murdoch was not a "fit person" to lead a major international company such as News Corp.
The MPs also said that he had "turned a blind eye and exhibited wilful blindness to what was going on in his companies".
On May 2, News Corp's board said that it had "full confidence" in Murdoch's ability to lead the company, despite the Parliamentary committee's findings.
"The Board based its vote of confidence on Rupert Murdoch's vision and leadership in building News Corporation, his ongoing performance as Chairman and CEO, and his demonstrated resolve to address the mistakes of the Company identified in the Select Committee's report," said News Corp.
But New York-based Amalgamated Bank and Jacksonville, Illinois-based Central Laborers Pension fund say that the board's backing of Murdoch shows that they cannot be relied upon to act in shareholders' best interests.
"Plaintiffs seek to obtain redress for News Corp's public shareholders for the harm caused by the board's bad faith failure of oversight," according to the complaint.
The investor's lawsuit has now been substantially amended since it was first filed in March last year, following another amendment in September.