On a Sunday the amount of traffic is relatively small, the council says
Controversial plans to close the A4 Portway, one of the main routes into Bristol, on summer Sundays are being considered by councillors.
Under plans put forward by the Liberal Democrats traffic would be re-routed across The Downs and Whiteladies Road.
"For a minor amount of inconvenience to some motorists this would be a fantastic opportunity for Bristol families," Cllr John Rogers said.
But the Association of British Drivers called the idea "absolute rubbish".
Spokesman Bob Bull said a plan to close the main road into the centre of Bristol from the motorway was "crackpot".
"There are a tremendous amount of areas around Bristol that are cyclist only, let them stay there and enjoy themselves.
"Closing major roads for cyclists is ridiculous," he added.
Under the proposal Ladies Mile across The Downs would also close on summer Sundays, a suggestion first mentioned in 2004.
Mr Rogers said Bristol was a city with ambition and it should be looking at ways of making it better - particularly at weekends.
"The idea of everyone being able to take their children and cycle along The Portway to Sylvan Way in a car-free environment enjoying the scenery is a really exciting opportunity - people have been talking about this for years.
"On a Sunday the amount of traffic along that road is relatively small. I'm keen we should look at these options - there are so many things we could do for our transport and leisure opportunities.
"I am happy to hear any ideas on how we can improve on the offer we have," he added.