St George's Healthcare NHS Trust in Tooting, South London, has been fined £5,000 and ordered to pay £6,432 after failing to take proper precautions over the management of asbestos.
The trust pleaded guilty to breaches of control of asbestos regulations at the City of London Magistrates' Court.
A Health and Safety Executive (HSE) investigation had found that it did not have an effective asbestos materials management system in place at The Groves residential block, which had asbestos containing materials within it.
Neither did it control the risk of exposure to asbestos fibre in the building, despite the fact that it had been made aware of its presence many times over a number of years.
HSE inspector Hazel McCallum stated: "It is disappointing when large organisations such as the trust put people at risk by not taking a responsible approach."
The inhalation of asbestos fibres can lead to serious illnesses, including the cancer mesothelioma.