In the past, US officials have kept discussions on the topic behind closed doors, for fear of embarrassing their hosts.
However, Mrs Clinton openly criticised Beijing's record on women's rights when she visited China in 1995, during the presidency of her husband, Bill Clinton.
Our correspondent says it remains to be seen if her new role will mean a change of tone.
Exports concern
On the economy, Mrs Clinton is expected to raise US concerns that China has artificially lowered the value of its currency to gain an advantage in exports to the US - its biggest market.
Also of concern to the new US administration of President Barack Obama are figures showing that China has become the world's largest single producer of carbon emissions.
Beijing says that as a developing nation, it cannot accept a cap on its emissions.
The outcome of talks between Chinese leaders on one hand and Mrs Clinton and US Special Envoy for Climate Change Todd Stern on the other, could affect the outcome of December's UN Climate Change Conference in Copenhagen.
The visit comes amid speculation North Korea is to test-fire another missile
Mrs Clinton is also due to discuss North Korea and attempts to get six-party talks on the North's nuclear programme back on track.
China is seen as Pyongyang's closest ally and the country most likely to influence the hard-line communist country's rulers.
Speaking in the South Korean capital, Seoul, she said the North should follow through on its commitment to get rid of its nuclear programme.
She said that South Korea's prosperity and democracy stood in stark contrast to "the tyranny and poverty across the border to the North".
"North Korea is not going to get a different relationship with the United States while insulting and refusing dialogue with the Republic of Korea," she said.
Shi Yinhong, Professor of International Relations at the People's University in Beijing, said that the two sides won't make demands on the other over conflicting issues but there will be discussions on differences.
"Both sides are prepared for this," he said. "The US's eager attitude to reduce the global economic difficulties and tackle global climate change issues will leave an impression on China but as to what measures China will take, that cannot be decided in one meeting."
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Mrs Clinton has a precedent to follow - it is her own
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