Towerbank Primary, in Portobello, was promised the additional space at the start of 2009, when the council confirmed funding for the work.
The project was originally due to be completed this year, but it has suffered a series of delays.
Members of the council’s planning committee have been recommended to approve plans for a three-storey classroom extension and new single-storey standalone nursery with dedicated outdoor play area.
The city’s education leader said the eight-classroom extension would make a “real improvement” to the school, which is one of the city’s most popular.
However, concerns have been raised over the height of the extension, overdevelopment, “poor quality” of design, parking problems and road safety.
Marion Williams, director of heritage watchdog the Cockburn Association, said: “We are very concerned by the lack of architectural ambition and poor quality of this application for additions to what is the most important and impressive building in this part of the Portobello Conservation Area.
“It is important that a scheme is devised which contributes positively to the local urban environment and enhances the existing infrastructure so as to ensure its long-term future. We therefore reluctantly wish to object to this application in the strongest terms as the community simply deserves better.”
A 16-signature petition from the residents of Wilson’s Park and Figgate Bank has also been submitted to the council.
In a joint letter of objection, they said: “We wish to emphasise that we are not opposed to the development of the Towerbank school site in principle and we welcome the improvement of the educational facilities in the local area.
“Our concerns relate to the way in which the development is currently configured, which has an unacceptable and disproportionate impact on nearby residential properties in Wilson’s Park and Figgate Bank.
“We would request that the plans are reconfigured to the advantage of all who hold a stake in the development of the immediate local area.”
Towerbank Primary has already had to sacrifice its library and music rooms to cope with the accommodation pressures.
City education leader Councillor Marilyne MacLaren said: “Towerbank Primary School has been in need of an extension for some time and I am delighted that the project has now reached this stage.
“Many of the concerns expressed during the consultation with the local community have been addressed through amendments to the proposed designs.
“If the plans are approved, the extension will make a real improvement to the environment of one of our most popular and successful schools.”
Councillors will vote on the plans on Wednesday.