The Libyan Investment Authority is seeking compensation from the bank and from Walid Giahmi, an alleged associate of Saif al-Islam Kadhafi, for what it says is money that it lost on trades between 2007 and 2009.
Societe Generale denied the "unfounded" claims by the LIA, which was set up in 2006 to handle Libya's oil revenues.
The Libyan fund's deposition to the High Court in London, of which AFP has obtained a copy, accuses the French bank of paying at least USD 58 million to Leinada, a Panamanian-registered company run by Giahmi.
The fund said in a statement: "The LIA states that the trades are void or unenforceable because of acts of bribery and corruption."
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It said: "There is no evidence of Leinada providing any legitimate services in relation to any of the disputed trades."
The French bank said in a statement to AFP: "Societe Generale disputes the unfounded allegations in the complaint by the LIA."
In January the Libyan fund launched a claim against US banking giant Goldman Sachs in London's High Court, accusing it of making USD 350 million profit on USD 1 billion worth of failed derivative trades.
Saif al-Islam, long his father's right-hand man and heir apparent, is in custody in Libya awaiting trial on a raft of charges stemming from the family's time in power.