Bolton also said:
Trump offered 'personal favours to dictators'
The Chinese leader is not the only authoritarian Mr Bolton accuses the president of pandering to.
Mr Trump was willing to intervene in criminal investigations "to, in effect, give personal favours to dictators he liked," Mr Bolton wrote.
According to the book Mr Trump offered help to Turkish President Recep Tayyip Erdogan in 2018 in a US investigation into a Turkish company over potential violations of Iranian sanctions.
The US president is said to have agreed to "take care of things" and that the prosecutors involved were "Obama people".
The Democrats should have gone further with impeachment efforts
In the book, Mr Bolton backs up Democrats' allegations that President Trump wanted to withhold military aid to Ukraine to pressure its government into investigating his rival Joe Biden. The claim sparked impeachment efforts against Mr Trump.
However, Mr Bolton criticises the Democrats in his book, saying they committed "impeachment malpractice" by just focusing on Ukraine. He argues that if they had broadened the investigation more Americans would have been persuaded that President Trump had committed the "high crimes and misdemeanours" necessary to be removed from office.
Mr Bolton does not say if the new allegations he makes are impeachable offences.
He declined to testify in the process when it was in the House of Representatives late last year, then was blocked from appearing in the Senate by Republicans.
John Bolton: Ten biggest claims in his Donald Trump book - BBC News