A court in the central city of Hebi tried Tao Liming, previously president of the Postal Savings Bank of China, as well as his subordinates Li Chuntai and Sun Lina, it said.
The state-owned Postal Savings Bank, a spin-off from China's sprawling post office system, boasts the country's biggest network of banking outlets.
Its website describes it as China's fifth-largest banking institution by client and deposit numbers.
The three men are accused of diverting 340 million yuan (USD 56 million) for investment to seek "personal profit", the Xinhua report said.
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Tao became head of the bank in 2007 but came under investigation for graft in 2012. He was formally arrested in December that year.
Chinese President Xi Jinping has pledged to root out high-ranking "tigers" as well as low-level "flies" in a much-publicised anti-corruption campaign.
Authorities have snared hundreds of officials in the drive, including former internal security chief Zhou Yongkang and Liu Tienan, once deputy director of the government's top economic planning agency.
But critics say there have been no systematic changes that could fundamentally root out graft in the one party state.