The civil suit claims three attorneys submitted bills for more than $200,000 to file an appeal of Burge's 2010 perjury and obstruction of justice convictions.
The union said it had contracted with just one of the attorneys to do the appeal for $60,000.
The suit also names a former union official for allegedly authorizing the payment.
Burge is currently serving a four-and-half year federal prison term for lying about his role in the torture of suspects while with the Chicago Police Department.
