A study carried out by disability organisation Vitalise commended The People's Palace, The Riverside Museum, Kelvingrove Museum and Art Gallery and the Gallery of Modern Art for their disabled access.
The charity rated 85 of the top 100 attractions in the UK, looking at factors including wheelchair access, disability and carer concession rates, the number of disabled toilets and parking spaces.
Vitalise chief executive Chris Simmonds said: "Congratulations to the Glasgow quartet on performing so well in our league table.
"You have clearly gone the extra mile for your visitors with disabilities."
While commending Glasgow on its accessibility, Mr Simmonds urged businesses to be more disability-friendly.
He said: "Our report and survey demonstrate that the UK's tourist attractions need to work harder, not only to make their premises more accessible to prospective disabled visitors, but also to be much clearer in what they are saying about accessibility."