But the large number of shareholder votes against Dell represents growing discontent about the company's performance under Dell's leadership, Rees said.

"It's rare for a chairman and CEO who founded a company to receive a significant no," Rees said.

"Shareholders could send a message that independent leadership is needed ... to improve accountability," Rees said, adding that the trade union will continue to encourage the board to establish changes in leadership.

Shareholders have lost tremendous share value under Dell's leadership as chairman, Rees said. The company's share price has fallen 66 percent in the past decade with Dell as the company's chairman, Rees noted.

Through the vote-withholding campaign, the AFL-CIO also hoped shareholders would hold Dell accountable for the SEC's allegations against the company for improper disclosure of the company's relationship with Intel and misleading financial practices.