According to the Mail on Sunday, former vice-chairman Stuart Neame has filed a member’s resolution ahead of the 19 October meeting.
He blames the board, including chief executive Jonathan Neame, his first cousin, for a reduction in profits and a fall in its share price.
“The profits have been pretty grim for the past five years and it is due to the management,” Stuart Neame told Financial Mail.
“Management has been terrible, there has been a gross failure of their part to take the company where it should be and they have made decisions such as spending £5m on a new computer system, which is a hell of a lot of money and is just £5m straight down the drain.
"The other shareholders will initially support the management, but they might change their minds when they see how much their investment has fallen.”
It is not the first time that Neame, who owns five per cent of the firm, has fallen out with his relatives. In 2004 he unsuccessfully took the brewer to an employment tribunal and tried to install his brother Roderick on the board.
Shepherd Neame unveils its full-year results on Wednesday (26 Sept) with analyst Peter Ashworth of broker Charles Stanley Securities stating the company is in "a strong position".