The bank also plans Kuwait, Oman and Yemen operations as part of its regional expansion.
Qatar National Bank (QNB), Qatar's largest bank by assets, said on Saturday it had opened an office in Libya as part of regional expansion plans.
The half government-owned bank will also open a branch in each of Kuwait, Oman and Yemen, the lender's acting Chief Executive Ali Shareef al-Emadi said in a statement.
Emadi said in January the lender would start operations in Yemen by July and in Oman in the third quarter.
Qatar National Bank would also open an office in Singapore, and is seeking as many as three operating licences in the Middle East and North Africa, he said.
Gulf Arab lenders are expanding outside of their home markets as they face more competition from domestic and international banks.
Arab economies are surging on higher oil prices, which quadrupled in the four years to July 2006. Libya is Africa's largest holder of crude-oil reserves.