US policy since 1979 has respected China’s stance on Taiwan, which it sees as a breakaway province.
But Mr Trump said that without concessions from Beijing on trade and other issues, he did not see why that should continue.
Relations with China became strained when Mr Trump took a phone call from Taiwanese Tsai Ing-wen.
Speaking in an interview with Fox News broadcast on Sunday, Mr Trump said: "I don’t know why we have to be bound by a One China policy unless we make a deal with China having to do with other things, including trade."
Mr Trump also said China was not co-operating with the US on its handling of its currency, on North Korea, or on tensions in the South China Sea.
Mr Trump said it was not up to Beijing to decide whether he should take a call from Taiwan’s leader.

For China, it is difficult to think of a more important issue in its relations with other countries than the One China policy.
Mr Trump suggested the One China agreement could be used as a kind of bargaining chip in negotiations on other issues, such as trade. But it is hard to image the circumstances in which that might be acceptable in Beijing.
It will become increasingly alarmed if the US president-elect continues to suggest American policy towards China is about to change.