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.

The head teacher of Sandown Bay Academy resigned and the board of governors was replaced earlier this year.
Academies Enterprise Trust (AET) said it intended to merge it with Ryde Academy to make "one great school".
It said falling numbers and the consequent impact on finances had prompted the decision.
Sandown Bay Academy came out of special measures two years ago, but is still seen as underperforming.
Pupil numbers have fallen to fewer than 1,000 from 1,252 in 2012.
In a statement, AET, the biggest academy chain in England, said: "It has been becoming increasingly difficult for the school to fund the teachers and the educational resources needed in order to provide the education we would all want for the students.
"We believe that merger offers the best option all round, and that out of these two schools we can create one really great one."
If approved, the principal of Ryde Academy, Joy Ballard, will oversee the transition between the two schools.
A spokesman said no decision had been made on whether to operate two campuses or on any job cuts.
A public consultation is to be held on the plans, with the final decision made by the government after the general election.
More than 600 staff are on a waiting list for parking, according to the trust running a West Midlands hospital.
[NEXT_CONCEPT]
A troubled Isle of Wight academy is set to merge with another school, its sponsor has announced.