The rebels, represented by lobby group NWOGaction, are backing the nomination of three directors to the board at the company's forthcoming annual meeting.
They said one of the candidates, Adam Reynolds, had identified a project and team to take the company into medical technology.
The investors have become concerned about the company's future following the falls in the oil price and the turmoil hitting the industry.
NWOGaction now represents investors holding 11.04% of the group, which focuses on Belize and Denmark.
In a statement, the action group said: "It is NWOGaction’s firm belief that the company requires a significant change in direction."
They added: "This is a radical departure from the company’s current business model, but with the various ills afflicting the oil & gas sector, NWOGaction is convinced such a change of course would be to the advantage of all shareholders."
In September, NWOG said it was in talks about seven new projects and was trying to attract farm-in partners for its Belize and Danish schemes.
It raised £3.5mln through a share placing and open offer to existing shareholders to fund existing projects, as well as working capital and the new schemes.
It follows an episode in which investor Chris Williams, otherwise known as "Chris Oil", claimed to have accidentally bought nearly half the company on his mother’s behalf, technically forcing her to make an offer for the entire company. She later had her stake reduced to 25.94%.
Some 342.3mln shares were bought at the end of April and whilst the initial stock market notification claimed this represented 10% of the company; it should have read 48.7%.