The Tory leader also said he was determined to maintain a "normal" family lifestyle if he won the next General Election.
But he displayed his ruthless streak by insisting he would not hesitate to sack shadow chancellor George Osborne, or other senior colleagues, if they were not up to the job.
In an interview with the Evening Standard, Mr Cameron said his faith ran "hotter and colder by moments" and he did not feel he had a "direct line to God".
"If you are asking, do I drop to my knees and pray for guidance, no," he said. "But do I have faith and is it important, yes. My own faith is there, it's not always the rock that perhaps it should be.
"I've a sort of fairly classic Church of England faith, a faith that grows hotter and colder by moments but... I suppose I sort of started life believing that one's individual faith was important, but actually the institutions of the church were less important.
"I do think that organised religion can get things wrong, but the Church of England and the other churches do play a very important role in society."
He went on: "I think that it's perfectly possible to live a good life without having faith, by which I mean a positive and altruistic life, but I think the teachings of Jesus, just as the teachings of other religions, are a good guide to help us through."
Questioned about his fears, Mr Cameron - whose disabled son Ivan died aged six earlier this year - said that the biggest one was of something happening to his family.
"That's fear number one, particularly as it has happened already, it is a sort of permanent fear," he said.
"The most natural thing in your life is to look after your little ones."
He said his other children seemed to have dealt with the death in a much better way than the adults: "They are amazing; they are able to remember Ivan with happiness in a way that adults find difficult. They say lovely things about where he is and what he's doing."
Mr Cameron said a terror of failure and letting others down also drove him on. "I've always thought that the fear of getting things wrong inspires me more than the wonder of getting things right," he added.
With the Tories in pole position to win the next General Election, Mr Cameron indicated he would try to get a better work-life balance than the current incumbent of Number 10.
"I'm sure although there are security restrictions in your life, you just have to battle for normality," he said. "If you spend your life in a poorly-lit bunker surrounded by your aides you are not going to make very good decisions.
"But I believe it must be possible to be a good father, good husband, normal person, a good party leader and, by dint of that, a good prime minister."
And he stressed that he would be willing to sack even close political allies if they did not perform well.
"I've done so before with other colleagues and I will do so again," he said. "With George, the answer is yes. He stayed in my shadow cabinet not because he is a friend, not because we are godfathers to each other's children but because he is the right person to do the job. I know and he knows that if that was not the case he would not be there.
"I think he had a very, very tough time last year. He really did suffer quite a lot of slings and arrows. But I have faith in him as a talented politician and a talented shadow chancellor and someone who has a great feel and understanding of politics and the great issues. I think he has come back in a very strong way."
Mr Cameron also confirmed that he had finally managed to give up smoking.
"I am now clean," he insisted. "But I still dream I have just had a cigarette and then have deep remorse on waking, until I realise it was only a dream. The yearning has gone. I have genuinely given up and do not even miss it."
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