Two areas of the city - Ashley/Easton/Lawrence Hill/Eastville/St George West and Southville/Bedminster/Windmill Hill - are being proposed for trials.
Major roads running through these areas, such as the M32 and Stapleton Road, in Easton, and North Street, in Southville, would be exempt.
The 20mph limits will not involve the introduction of any physical traffic-calming measures, such as speed humps or chicanes.
Executive member for transport and sustainability Jon Rogers said: "The primary aim is to make walking and cycling in these communities safer and more attractive to more people.
"Reducing the speed limit to 20mph should also help to reduce the number of road accidents.
"We will be monitoring the success of the two pilot areas and listening to comments before we look at whether they could be extended to other parts of the city.
"We are not expecting the schemes to cause any significant delays to drivers."
Mike Popham, Prospective Member of Parliament for Bristol East said "This reinforces the Liberal Democrats' strong green agenda. 20 mph makes sense not just for road safety but also promotes cleaner air, less congestion and more people taking up cycling and walking. No doubt it will reduce fuel costs as cars stop and start less."
The council is seeking the public's comments before September 30.
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