Hillhead and Jordanhill club applied for planning permission to build a new spectator stand at its ground in Hughenden Road in the West End.
But the move resulted in objections from Dowanhill, Hyndland and Kelvinside community council, local councillor Pauline McKeever and five neighbouring residents.
They raised fears about anti-social behaviour, which was a problem before the previous stand was demolished, insufficient parking and traffic problems.
Neighbours complained the appearance of the new stand will be unsightly and out of keeping with its surroundings, would create noise and that mature trees would be felled. But councillors passed the plan without comment when it came up at the city council planning committee.
A report from Richard Brown, the council's executive director of development and regeneration, said the new covered stand, which will be less than three metres high and three deep, will seat 213 spectators and three wheelchairs in four rows.
And he insisted the stand would not affect the look of the conservation area as it had a background of the pitch or modern flats.
Mr Brown said the trees which will be removed are not covered by a tree protection order and will be replaced with three suitable new trees.
He added: "As always, residential amenity must be considered but the proposed stand is to house the spectators who already come to view the sports played on the existing pitch at an existing club."
The rugby club, which is known as The Hills, has said it will be used for around 17 rugby matches during the season.
Mr Brown said: "A larger stand which was demolished about a year ago on the sports club land appears to have given shelter to people taking part in anti-social behaviour which had been reported to the police. Since the stand was demolished, the incidences of this behaviour appear to have decreased according to the objections.
"Local residents are concerned the new stand would increase this level of anti-social behaviour."
But the council boss pointed out anti-social behaviour is a matter for the police and is not a planning issue.
He added: "The proposals is to erect a stand for spectators and a stand is not the cause of anti-social behaviour. There is no indication the levels of spectators will increase, so the proposed new stand should not have an impact on traffic or parking."