Although no details surrounding the breaches of the Health and Safety legislation were given to the city's Crown Court, it is understood it relates to an incident in January 2011 involving a subcontractor who came across asbestos while working at the Belfast City Hospital.
In all, the Trust's Estate Director Mr Eamon Malone pleaded guilty on their behalf to three charges involving the breaches.
Two related to failing to ensure the welfare and safety of their employees, and secondly a similar count referring to non-employees of the Trust.
Another charge involved the Trust's failure to ensure that the locations of asbestos materials are notified to anyone who may have to work in that area, and possibly disturb the hazardous items.
Prosecutor Gareth Purvis and defence QC Gerald Simpson said there was information they wished to gather and consider before sentence is passed early next month.