Barclays has "repeatedly let down society with its conduct" the Church of England has said in its annual report.
The church, which holds a small stake in Barclays, criticised the bank's actions in recent years, which has seen it lumbered with scandal and several resignations.
It now wants to see a "fundamental turnaround in culture" within the bank.
The church operates an ethical investment policy, which states it seeks to avoid activities that are "materially inconsistent with Christian values".
As part of that policy it said its commissioners had started an intensive engagement with Barclays in order to seek robust assurance that the company is making "a determined and successful effort to effect a fundamental turnaround in culture".
Barclays was caught up in the Libor scandal last year that led to the resignations of its chairman and chief executive.
Antony Jenkins, the bank's current chief executive, has pledged to clean up the bank's image under his transform programme.
By Claire Archer