The suit alleges that armslist.com, the Internet broker who helped match shooter Dmitry Smirnov with the gun's seller, failed to perform a background check on Smirnov, who pleaded guilty to the killing.
Smirnov, Vesel's ex-boyfriend, killed her in April 2011, after tracking her with a GPS device that was glued to her car.
Vesel, 36, was shot 12 times as she tried to run from Smirnov in the parking lot of an Oak Brook, Ill., corporate park. They had only dated for a few weeks - she broke up with him 2 1/2 years before she was gunned down.
Smirnov admitted stalking and killing Vesel because of the break-up.
The Brady Center to Prevent Gun violence is bringing the lawsuit on behalf of Vesel's brother, Alex.
"The complaint alleges that the website's design facilitates illegal gun sales to unlawful gun buyers, with no background checks, and no questions asked," Brady Center attorney Jonathan Lowy said.
On its website, armslist has a disclaimer stating users must comply with all laws, adding armslist does not get directly involved transactions.
Lowy said that's not good enough.
"A lawsuit like this can send a message," he said.
CBS Chicago says finding a number for, or reaching any employees of armslist is almost impossible, so the station was not able to get in touch with anyone from the website for comment.
Smirnov was sentenced to life in prison for killing Vesel.