The state is asking a Common Pleas judge in Cuyahoga County to make the bar pay the $49,000 in fines it has racked up in the three years since Ohio banned smoking in workplaces.
Health inspectors have issued the Suburban Inn at least 13 violations since 2007, the most of any establishment in Cuyahoga County.
"Suburban is No. 1," said John McLeod, director of environmental health services at the Cuyahoga County Board of Health.
"It's for your customers. It's for your workers. It's for their health and their wellness. And I just think they chose blatantly not to comply with the law."
Second-hand smoke is proven to cause a myriad health problems, including cancer and heart disease.
One of the violations was issued last November after Channel 3 News used undercover cameras to videotape bartenders and customers openly smoking in the Bagley Road bar, McLeod said.
Rose Summa and Richard Amarosa, who own the Suburban Inn, could not be reached for comment.
This is the first smoking-ban-related lawsuit filed in Cuyahoga County on behalf of the state Health Department by the Attorney General's Office.
The Attorney General's Office has filed on four other establishments since the ban went into effect, said spokeswoman Kim Kowalski.
Two of those lawsuits are pending and one is under appeal after a judge ruled the way the ban was enforced was unfair.
The state has collected more than $20,000 in fines as a result of the lawsuit filed against J's Sports Bar in Cincinnati.