It would apply to sidewalks and other public areas in a 17-block area around Todos Santos Plaza.
Critics say police have more important things to worry about. But Concord Police Chief Guy Swanger says enforcement would start with education.
"After that we'll start the warning process and I think people will eventually get to self-police themselves. In those instances where there is some disobedience, we can address it by citations. I believe that it'll only take a few months of that kind of enforcement before word starts to get out."
The ban was requested by local businesses that complained about groups of smokers congregating around the plaza.
A final vote on the measure is expected next month. It would make Concord the first city in Contra Costa County to have a downtown-only smoking ban.
Other Contra Costa cities have stricter smoking rules, banning smoking within 20 feet of doorways citywide.