The suit, filed last week in US District Court for Eastern Michigan on behalf of Jeffery Klimas, charges that the cable TV and Internet service provider illegally collected the Web-surfing habits of its users from December 2001 to February 2002.
Comcast has denied the charge.
The suit was filed out of an incident last February when Comcast revealed it was collecting the surfing habits of its customers.
Comcast president Stephen Burke said in a statement at the time that the cable company had collected and stored IP and Web address information for about six weeks. He added the information was "never connected to individual subscribers". The statement said the information has been purged in the interest of privacy.
In its statement, Comcast repeated its assertion that it never identified users.
"Comcast respected the privacy of our high-speed Internet subscribers and has not in any way compromised their privacy or linked Internet usage data to personally identifying information about any specific subscriber," said the company statement.
But Klimas' attorney, Steven Goren, rejected that statement. He said Comcast claimed that it only tracked data according to IP address and not by specific names.
Goren said it was important that companies be stopped from being able to say that because a name is not attached to a specific piece of data, and therefore, that the data does not identify an individual.
He said that would be like the phone company saying it did not track individual data by actual name only by telephone numbers. He said IP addresses are personally identifiable numbers.
"I am not given much solace by the fact that they did not happen to run the software program that would have linked the names to the numbers before being caught," Goren said.
In the suit, Goren asked that the company be forced to pay $100 (£69) per day for each violation of privacy or $1,000 (£921) per customer, whichever is higher. He alleged that at least one million customers are included, so the damages could reach as high as $1bn.
Goren said that once the suit is served on Comcast, the case will enter the discovery phase. He said it would probably be several months before the case is resolved.