Biglari has twice pushed for shareholder votes on new leadership and twice shareholders have turned down the candidates by large majorities, The Wall Street Journal reported Monday.
Biglari owns about 19 percent of the chain, which is a combination retail store and restaurant chain.
In the latest attempt to place two nominees on the board, Lion Fund II, a hedge fund in San Antonio, Texas, submitted nominations on Biglari's behalf.
The board turned them down.
"Despite being rejected by a significant margin of the vote of our shareholders in each of the last two years, Mr. Biglari has again chosen to re-fight the battle to elect himself and Mr. [Philip] Cooley [vice chairman of Biglari Holdings]," said Cracker Barrel Chairman James Bradford in a statement.
The board, however, announced Monday Martha Mitchell, a board member since 1993, would retire when her term ends.
Cracker Barrel has attempted to buy Biglari's shares, but he turned down their $300 million offer, the Journal said.
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