Anderson said the archdiocese has released the names of only two of those problem priests.
"Catholic bishops in Illinois have been hiding the names, the identities of religious order priests who have been publicly accused of child sexual abuse," he said Thursday during an a online news conference.
"It raises the question: How many more kids are going to get hurt because of the non-disclosure?"
The Chicago archdiocese declined to comment on Anderson's demand.
Cardinal Blase Cupich has demanded for more than two years that Catholic religious orders which operate in his territory fully disclose to him any information about their members who now face or have faced accusations of child sexual abuse.
The Archdiocese of Chicago, which grants the orders permission to operate within its jurisdiction, has refused to say what it knows about predatory religious order clergy.
Some religious orders publicly list credibly accused clerics, while others don't.
Religious orders have their own leaders and operate relatively freely within the dioceses, though they need permission from the local bishop, such as Cupich, if they engage in public ministry in a parish, at a school or hospital or in some other charitable endeavor.
Photos: Illinois' Starved Rock State Park brings together history and nature
Three Chicago men killed in a explosion while fishing and making a fire unwittingly picked up an explosive rod that was left behind during a demolition project near Starved Rock State Park, according to lawsuits.
The families of three men who were killed in an explosion near Starved Rock State Park in May filed suit Wednesday afternoon against several construction and blasting companies that, the complaint alleges, left behind an undetonated explosive rod that the men accidentally ignited.