Normally applications require a declaration of any past dealings with police but Cardinal Vincent Nichols said people should not be compelled to disclose their conviction.
Speaking at the Conference of Prison Chaplains, he said stopping the practice would allow convicts to "put their past in context and show who they really are".
"Of course convictions have to be disclosed and where necessary DBS checks undertaken," he said. "But people should not be written off without a hearing for actions in the past which may no longer have a bearing on their future."
He added that criminals leaving jails must have support and employment.
"It is hard to envisage the crushing disappointment of someone who has worked hard to move away from crime and learn new skills, only to be rejected for job after job and never even given the opportunity to explain how he or she has changed since being convicted years before.
"That is not just devastating for the individual - it deprives employers of potentially excellent and able workers and denies society working taxpayers."
Cardinal Nichols stressed that jobs like teachers and police officers would still require full disclosure but suggested even the Church could stop asking for an applicant's past.
"Over the coming year I look forward to discussions about how the Church can ban the box in our own employment practices, while taking all the necessary steps to ensure that safeguarding is never compromised.
"I personally appeal to all employers to take this step and give people a fair opportunity that will benefit our society."
Elsewhere in his speech Cardinal Nichols offered the Church's help in prison reform to transform "prisons from places of despair to places of redemption".
The Ministry of Justice has been contact for a comment.
