The argument stems from use of the term Globex, which is CME's electronic trading system, which dates back to 1992. CME says it has a trademark for the name, Crain's Chicago Business reported Thursday.
Global Foreign Exchange, on the other hand, is also known as Globex FX.
Besides use of the name, CME said the Canadian firm seized domain names that purposefully made use of similarities between the two companies.
The lawsuit filed in the U.S. District Court for the Northern District of Illinois said "The intent of Globex FX in registering the Globex FX domain names was to profit from the goodwill and value associated with the Globex marks, causing harm to CME."
The lawsuit asks Globex FX to pay profits it may have made by use of the similar trademark and domain names.
CME said it asked Globex FX to take corrective actions in 2008, but the company did not comply with the request.
Duggar sisters unveil Christian dating rules in new book
LGBT community has 'bullied the American people': Bachmann