Mr Bush also called Mr Rumsfeld "an arrogant fellow" with "swagger".
Mr Cheney was vice-president and Mr Rumsfeld was defence secretary under George W Bush.
"I don`t like what he did, and I think it hurt the president having [Mr Rumsfeld`s] iron-ass view of everything," Mr Bush said, according to an article in The New York Times that cites the biography`s author, Jon Meacham.
"There`s a lack of humility, a lack of seeing what the other guy thinks. He`s more `kick ass` and `take names, take numbers`. I think he paid a price for that."
Jeb Bush has had plenty of drama in his presidential quest recently, with poorly reviewed debate performances and sinking poll numbers leading to a recently unveiled "Jeb can fix it!" campaign reboot. Now, thanks to his father`s new biography, he is likely to face questions once again about his family`s tangled presidential dynasty.
Jeb has repeatedly asserted that he`s his own man and is forging an identity distinct from that of his presidential relatives, but that hasn`t stopped reporters from pressing him on his views of George W Bush`s time in the White House, including the wisdom of the Iraq War. His answers, to put it kindly, have been less than clear and consistent.
It`s only a matter of time before Jeb is asked whether he agrees with his father`s view that George W occasionally used overheated rhetoric and relied too heavily on bellicose advisers like Vice-President Dick Cheney. No matter how he answers, questions like these will push him off his desired message at a critical time in his campaign.
Mr Cheney, Mr Bush said, changed in the time between serving him and his son.
"He just became very hardline and very different from the Dick Cheney I knew and worked with," Mr Bush reportedly said, attributing this to the 9/11 attacks.
He told author Jon Meacham that Mr Cheney was "iron-ass" and had acted too independently of his son in matters of national security.
Of his son, Mr Bush said he would often worry about the former president`s rhetoric.
Citing the "axis of evil" reference in the 2002 State of the Union address, he said: "You go back to the `axis of evil` and these things and I think that might be historically proved to be not benefiting anything."
Author Jon Meacham interviewed Mr Bush for the book Destiny And Power: The American Odyssey Of George Herbert Walker Bush.
