Council bosses in the capital announced this week late-night shoppers would be able to park cars free in the city centre after 5pm in an attempt to attract people to Princes Street.
The no-charging time will run from December 2-28.
Now Neil Greig, director of policy at the Institute of Advanced Motorists, is backing calls for Glasgow to drop its parking charges after 5pm in the run-up to what is normally the busiest time of the year for the retail industry.
Mr Greig said: "People like incentives and a good deal, so dicsounted parking should have a very positive impact and encourage more shoppers to the city centre.
"It is worth trying because we need to be getting as many people as possible into Glasgow city centre.
"Parking charges are a very big issue in Glasgow and Edinburgh and I am sure this kind of scheme can have only a positive effect."
Business bosses have previously called for charges to be reduced in an attempt to encourage shoppers back into the city centre.
Earlier this month, Glasgow's biggest retailers started staying open until 7pm on week nights in an attempt to boost business.
More than 200 shops in Sauchiehall Street, Argyle Street and Buchanan Street have extended their hours.
As reported in the Evening Times in May, retail chiefs hope later opening hours will transform Glasgow's shopping culture.
A Glasgow City Council spokesman said: "The council has in the past offered free parking at strategic times to bring people into the city and away from out of town shopping centres.
"We are discussing the matter with the Chamber Of Commerce to look at potential opportunities to do this again."