Councillors have slammed leisure bosses for allowing a pillar at the Gallery of Modern Art to become covered in green algae.
It is believed a leaking pipe caused water to run down the pillar, creating a breeding ground for algae.
And although Glasgow Life, which is responsible for the building, claims it has fixed the problem, the building has not yet been cleaned.
Martin Docherty, SNP councillor for Anderston and the City Centre, said: "I noticed the state of the building when I was walking past recently.
"This shows a complete lack of care for what is a prominent city building – the pipe was leaking for about four or five years – it's no wonder the pillar has ended up in this state.
"The gutters should be cleaned twice yearly and, if they are not, I would be asking questions as to why not.
"Frankly, it looks disgusting."
Museum bosses claim the source of the problem has now been fixed but the column has still not been cleaned.
A spokesman for Glasgow Life, an arm's length body of the council, said ways to clean up the pillar were being considered.
But a second city councillor said that response is not good enough.
Graeme Hendry, leader of the SNP on the city council, added: "Where GoMA sits is the postcard bit of the city centre.
"If it was Kelvingrove or the Transport Museum it would have been cleaned up yesterday.
"GoMa is clearly not high enough on the list of priorities, even though it is in the city centre and a draw for tourists."
A spokesman for Glasgow Life, said: "We are looking at solutions for permanently removing the algae.
"The algae has not caused any damage to the building."