He said the extremist group were just 2km away from the capital city and that "things are so bad".
IS has been killing and persecuting tens of thousands of Christians as it takes over large parts of Iraq and Syria.
In a post on Facebook he wrote: "They said it could never happen and now it almost has.
"Obama says he overestimated what the Iraqi Army could do. Well you only need to be hear a very short while to know they can do very, very little."
Meanwhile President Barack Obama said he 'underestimated' the threat posed by IS and didn't realise the Syrian civil war would help militants regroup and get stronger.
Canon Andrew White is the vicar of St George's Church, Baghdad; the only Anglican church in Iraq.
Speaking of his concern for the capital city on Premier's News Hour he said:"These people are coming towards us.
"We need people on the ground who can protect us and there's nobody.
He also called for British troops to be once again deployed on the ground in Iraq.
When asked the question he said: "With my British hat on, no I don't because we'll probably see a huge number of deaths.
"With my Iraqi vicar hat, yes I do, because my people need protecting and at the moment they have no protection whatsoever."
Hear the full interview with Canon Andrew White here:
