The chief executives body is introducing a code of conduct for members, which will include standards on conduct and personal performance.
It has set up a working party to develop the code, and will launch a consultation of members on the proposals next month.
Nick Aldridge, director of strategy at Acevo, said: "If we are claiming to be the guardians of standards for leaders in the sector, then we need to set those standards and show we take them seriously."
He warned that those failing to live up to the standards could be removed from the membership: "If we find that someone does not have any professional integrity, then we have to consider if we want to have them as a member."
Maria Aguilar, director of human resources consultancy HR Services Partnership, said: "If Acevo is going to say that to become a member you do not only need to pay your subs but also provide evidence that you meet these standards, that could make a difference. But it must have teeth."
If Acevo members give the green light to the proposals, the code could be introduced by September. Members will need to agree to the code when renewing their subscriptions.
The news comes after a YouGov poll revealed that public trust in charity bosses had taken a tumble.
The survey revealed that the number of people who trusted charity chief executives to tell the truth had fallen by 10 per cent to 64 per cent in the past four years.