Dr John Sentamu spoke against the policy, which allows independent schools to be set up with state money, saying it benefited the well-off and diverted desperately needed money away from the state sector.
'Free schools' was the flagship policy of former Education Minister Michael Gove as he sought to reform the education system.
But the clergyman says it only helps those who already have "means and ability" and does not tackle the root problems in schools.
The archbishop called it a "failed attempt" to bring back more grammar schools.
This latest criticism of the government comes just days after Dr Sentamu said the poor are being left behind in Britain.
He accepted his thoughts on free schools would be seen as "political" but he insisted they were not "party political".
The Telegraph newspaper says Archbishop John was speaking about the success of some academy schools when he added: "What I haven't bought is the idea that we should have free schools.
"Because the ones that have gone for free schools in the majority are people with means and ability ... I think that is just a confusion of policy.
"What should have happened is that the Government should have invested all that money in raising the level of achievement in schools that are less achieving, not by putting in these so-called competing places."
"What I don't actually think should happen is that in the ... sector of the nation where you are providing free education for everybody you should then create another similar school competing with another.
"If I am being very blunt I think it was a sort of failed attempt to create grammars.
"Of course that would be denied [they would say] that was never the intention, but I cannot see why in East Hull for example when you have now got a fantastic secondary as an academy, achieving now about the national average, you would want to create another free school there.
"To me the attempt is to make sure that every child in England can read, can write, can add, can subtract, can speak standard English and [have] all the possibilities. And [in] the delivery of all of this, it seems to me, central government has got to stop meddling.
"I mean they've really been meddling for a very long time and they've never listened to professionals actually.
"They come in with their policies and they are going to impose it."