The organisation contacted the Charity Commission in October last year after it discovered that a grant of £10,165 had been awarded to a member of its national council.
The commission's subsequent investigation revealed that a company linked to one of the trustees had also received a £3,000 grant from a programme that is administered by the charity, and another trustee had applied unsuccessfully for a grant of £4,650.
The regulator's report on the investigation, published last week, says the trustee had applied for the grant in good faith and had been asked to repay it in full. The grant application included a CV with details of the person's trusteeship, it says.
"The charity has confirmed that it has introduced changes to its systems to ensure that applications made by charity trustees are picked up in future," the report says.
The commission also advised Arts Council England to improve its induction processes for trustees and provide them with better training on their responsibilities and the charity's governing document.
"The charity has informed us that it has updated its induction programme for new charity trustees to ensure that the need to register and manage conflicts of interest is clearly explained and understood," it says.
A statement from the charity said: "The Arts Council reported this irregularity to the Charity Commission as soon as it was discovered.
"The commission has acknowledged the full cooperation of the Arts Council and concluded that no further payments have been made to trustees.
"It is also satisfied that appropriate policies and procedures have been updated, which will avoid an error of this kind happening again."
A Charity Commission spokeswoman said the council could only make grants to trustees with the express permission of the commission, which dealt with such applications case by case.