Speaking during a visit to Bristol Cathedral, the Most Reverend Justin Welby said he sometimes asks himself whether God exists.
The archbishop explained that he usually has these thoughts while out jogging. He said: "I mean, there are moments where you think 'Is there a God?', 'Where is God?'"
He admitted that these comments should not usually come from the leader of the Anglican Church, but added: "I love the Psalms. If you look at Psalm 88, that's full of doubt."
He told the congregation: "The other day, I was praying over something as I was running and I ended up saying to God, 'Look, this is all very well, but isn't it about time you did something, if you're there?' Which is probably not what the Archbishop of Canterbury should say."
He added: "It is not about feelings, it is about the fact that God is faithful and the extraordinary thing about being a Christian is that God is faithful when we are not."
Welby admitted that Christians can struggle to understand why God allows suffering but explained that they don't have to find reasoning in everything.
"We turn the tide in a number of ways," he said. "We know about Jesus, we can't explain all the questions in the world, we can't explain about suffering, we can't explain loads of things, but we know about Jesus.
"We can talk about Jesus. I always do that, because most of the other questions I can't answer."