Great Ape Protection and Cost Savings Act of 2011 – Prohibits: (1) conducting invasive research on great apes; (2) possessing, maintaining, or housing a great ape for the purpose of conducting invasive research; (3) using federal funds to conduct such research on a great ape or to support an entity conducting or facilitating invasive research on a great ape either within or outside of the United States; (4) knowingly breeding a great ape for the purpose of conducting or facilitating such research; (5) transporting, moving, delivering receiving, leasing, renting, donating, purchasing, selling, or borrowing a great ape in interstate or foreign commerce for conducting or facilitating such research; and (6) transferring federal ownership of a great ape to a non-federal entity unless the entity is a suitable sanctuary. Defines “great ape” as any chimpanzee, bonobo, gorilla, orangutan, or gibbon. Defines “invasive research” as research that may cause death, injury, pain, distress, fear, or trauma to great apes, including drug testing or exposure to a substance or isolation, social deprivation, or other experimental manipulations that may be detrimental to the ape’s health or psychological well-being. Requires the Secretary of Health and Human Services (HHS) to effectuate the permanent retirement of all great apes that are owned by the federal government and that are being maintained in any facility for the purpose of breeding for, holding for, or conducting invasive research. Sets forth civil penalties for violations of this Act. Establishes in the Treasury the Great Ape Sanctuary System Fund to be administered by the Secretary for construction, renovation, and operation of the sanctuary system for surplus chimpanzees.