The final vote is expected to take place on Feb. 22. If it passes, it goes into effect Jan. 1, 2012.
West Hollywood already prohibits smoking inside restaurants, bars and workspaces.
The proposed ordinance would extend that ban to include outdoor patios and other open-air spaces.
Some business owners are opposed to the plan, saying they'll lose customers to nearby Hollywood.
But proponents of the ban say cities like Beverly Hills, which have passed similar bans, have seen business go up.
Steven Gallegos of the Coalition for a Tobacco Free Los Angeles County pushed hard for the city to pass the ban.
"Here in L.A. County, the smoking prevalence rate is 10 percent that does smoke," Gallegos said.
The city council is considering an exemption for night clubs and bars.