Glasgow Sheriff Court heard NHS Greater Glasgow and Clyde (NHSGGC) failed to properly manage the risk of asbestos in a neurology plant and switch room at the Southern General Hospital.
The court was told that three surveys, used to identify and manage asbestos containing materials (ACMs) in the premises, had been carried out in the room.
In all three, the same ACM in the ceiling of the room was identified as "high risk" and the recommended action was "removal and environmental cleaning".
In March 2011 a specialist company carried out a further survey, which found several highly damaged ACMs, debris from the original ACM in the ceiling, that posed a "high risk".
The room was sealed and background monitoring tests showed a high level of air contamination and the matter was reported to the Health and Safety Executive (HSE).
The probe found that the health board had not taken any action over the asbestos since the original survey discovered it in 2004.
After the case, HSE Inspector Aileen Jardine, said: "The dangers posed by the presence of asbestos are clear. There is no known 'safe limit'."
A spokeswoman from NHSGGC said: "We accept that our robust asbestos procedures fell short of the standards we strive to maintain. We have taken rigorous action to reinforce our asbestos procedure."