The former president of the Irish Farmers' Association, Mr Joe Rea, is seeking to organise a group of Greencore farmer shareholders to push for changes on the board of the company.
He was speaking after heated exchanges at the company's annual general meeting in Dublin yesterday.
Mr Rea and several other shareholders said the board had not displayed enough "vision" in recent years and should now appoint employee and farmer representatives.
Another shareholder said the board should examine why there was not a single female board member.
Mr Rea claimed the company's investment in US sugar group Imperial Holly had proven to be "dismal" and he suggested that bad decisions were being made by a board "filled with accountants".
The chairman of the company, Mr Bernie Cahill, said the board would examine the concerns of Mr Rea and other shareholders but he pointed out there were currently no vacancies at board level.
The exchanges about the composition of the board followed other critical comments from shareholders about the company's share price, which has fallen sharply in the last few months.
Chief executive Mr David Dilger said that while the performance of the shares was "disappointing", Greencore had performed well when measured alongside its "peer group".
Several shareholders expressed anger at the way the meeting was chaired by Mr Cahill. One accused him of ignoring shareholders' comments and being deliberately evasive.
Earlier Mr Dilger told the meeting Greencore was confident that by moving into the fast-growing segments of the food sector it would produce "greater shareholder value".
:quality(70)/cloudfront-eu-central-1.images.arcpublishing.com/irishtimes/VR3765MFOBH2NMV2QNICYDF67M.png)