Residents living around the Good Hope Hospital in Sutton Coldfield have said cars are being illegally parked on local streets by staff and patients.
Paul Quinsey, head of technical services, said the hospital is looking at demountable parking decks above existing car parks as one solution.
He said there are currently 626 staff waiting for a parking space.
Roger Bayliss, who had an appointment for an X-ray at the hospital, said he spent more than an hour looking for a parking space.
He said: "I would have abandoned my appointment had I been able to turn around and get out of the hospital, but the traffic was so gridlocked all across the site there was absolutely no option but to sit and wait."
Conservative councillor David Pears, who represents the Sutton Trinity Ward which covers the Good Hope hospital, said residents had put up with parking problems for "far too long".
He said: "We've met with the hospital, we've got the MP involved, but it just seems the hospital is unwilling to spend money on a scheme that will make life easier for the residents."
Mr Quinsey said the hospital is working alongside its publicly elected governors and staff to see how it can address the current issues around parking.
He said a plan to set up a park-and-ride scheme had been rejected because of its affordability and long transfer times.
More than 600 staff are on a waiting list for parking, according to the trust running a West Midlands hospital.