Dr Jennifer Armstrong said NHS Greater Glasgow and Clyde was working to improve accident and emergency waiting times and avoid delays to treatments.
She said she hoped a behind-the-scenes BBC documentary at Queen Elizabeth University Hospital would highlight the "incredible" work undertaken by staff.
There have been concerns about the hospital since it opened two years ago.
The hospital, which is one of the biggest in Europe, has consistently had some of the poorest waiting time figures for A&E in Scotland.
Concerns have also been raised about workload pressures and the number of operations cancelled because of a shortage of beds.
Dr Armstrong acknowledged the problems were "unacceptable", but said the hospital was performing some of the most advanced medical treatments in the world.
The new series of "Scotland's Superhospital" starts at 21:00 on BBC One Scotland.
An NHS director has apologised to patients who have experienced problems at Scotland's largest hospital.