Madeleine Albright said the president's use of Christian rhetoric and belief in the "absolute truth" was worrying.
"Some of his language is really quite over the top," she told Reuters on Sunday during a trip to London to promote her book, The Mighty and Almighty, which examines religion and world affairs.
"When he says 'God is on our side', it's very different from (former US President Abraham) Lincoln saying, 'We have to be on God's side'."
"I worked for two presidents who were men of faith, and they did not make their religious views part of American policy," she said, referring to Jimmy Carter and Bill Clinton, both Democrats.
Bush, a Republican, has said that his faith informs his decisions as president. He says, for example, that he prayed to God for guidance before invading Iraq.
"President Bush's certitude about what he believes in, and the division between good and evil, is, I think, different. The absolute truth is what makes Bush so worrying to some of us," Albright said.
Some Muslims have accused Bush of waging a crusade against Islam.
"I worked for two presidents who were men of faith, and they did not make their religious views part of American policy"
The White House says it has nothing against Islam, but against those who commit terrorist atrocities in its name.
In her book, Albright recalls how Bush, while he was governor of Texas, told Christians he believed God wanted him to be president.
She quotes from his speech to his party convention of 2004, when he told Republicans: "We have a calling from beyond the stars to stand for freedom."
Worse than Vietnam
Albright, 69, who was secretary of state under Clinton from 1997 to 2001, says the war in Iraq "may eventually rank among the worst foreign policy disasters in US history".
She describes it as arguably worse than the Vietnam War, not in terms of the number of people killed but because of the volatility of the Middle East.
She also worries at "the growing influence of Iran" in the region and said sectarian violence between Shia and Sunni Muslims could escalate into an all-out "Arab-Persian conflict".
"We should not be contributing to what is a long historical struggle between the Sunni and Shia," she said.
Asked about her own beliefs, Albright said she had "a very confused religious background".
Born and raised a Roman Catholic in Czechoslovakia, Britain and then the United States, she converted to Anglicanism when she married and only later in life discovered she had Jewish roots.
It is this legacy which makes her wary of any religion which claims a monopoly on truth, she said.