Leeds City Council want to make the city centre a better environment for pedestrians and cyclists.
A map on the council's website shows the vast majority of the roads in the city centre coming under the new speed limit, with the exception of Loop Road and sections of adjoining roads.
A document explaining the council's reasons for the proposal read: "The introduction of a 20mph speed limit within the city centre contributes towards creating a safe and forgiving environment that can be enjoyed by all road users.
"This approach is a well established element of Leeds City Council's programme of road casualty reduction and sustainable travel.
"Although the issue of pedestrian casualties in the city centre is complex and subject to multiple causation factors, a city centre 20mph speed limit would go some way towards redressing the balance in favour of a more pedestrian and cyclist friendly environment and reducing the domination of traffic."
Evidence from other cities shows that 20mph zones have helped reduce casualties, particularly among vulnerable road users.
"The introduction of a 20mph speed limit in the city centre will have the added benefit of raising the profile of the lower speed limits and will help make travelling at lower speeds through urban areas more of a social norm," the document adds.
The plans do no include the Lopp Road as it has "a distributary function and is an essential part of the network that serves to carry and circulate the majority of traffic movements around the city centre core".
"The city centre loop experiences high traffic volumes and has road characteristics that are more in keeping with the existing speed limit," the document adds.
"Excluding the loop from the proposed 20mph zone also further emphasises to all road users the change in road characteristics."
If approved, the plans would complement other big changes to the layout of the city centre, including the ongoing works to improve The Headrow, pedestrianisation around the Corn Exchange, as well as road closures at Merrion Street East, Greek Street and Cookridge Street.
Members of the public can make comments or lodge objections about the application before the deadline at noon on Friday, January 24.
Almost 100 20mph zones were rolled out around Leeds earlier this year, in addition to a longstanding programme introducing similar zones which has been running since 1990.