High on his list of priorities are discussions about economic sanctions against Iran meant to deter Tehran from proceeding with an alleged nuclear weapons program.
China, however, bought 11 percent of its oil from Iran in 2011, an increase from previous years.
The day before Geithner's arrival, Vice Foreign Minister Cui Tiankai said problems with Iran "cannot be resolved by sanctions alone."
He also said, "We should not mix issues with different natures," referring to nuclear weapons and "regular economic and trade relations."
The second issue at the top of Geithner's priority list is currency exchange rates. China, however, has long defended its currency policy, saying a stronger renminbi would have little impact on the trade imbalance between the United States and China.
Besides, "Other currencies are dropping against the U.S. dollar right now," pointed out Li Xiangyang, the vice director of the Institute of World Economics and Politics at the government-sponsored Chinese Academy of Social Sciences.
Geithner may find agreement in a discussion on how to prevent the European debt crisis from dragging down the global economy, the Times said.