Commission to Verify Iranian Nuclear Compliance Act This bill establishes in the legislative branch the Commission to Verify Iranian Nuclear Compliance which shall: (1) continually verify that the Islamic Republic of Iran is complying with its obligations under the Joint Comprehensive Plan of Action (JCPOA); (2) continually assess the adequacy of JCPOA safeguards to ensure that Iran's permitted activities are not being used to further nuclear-related military or nuclear explosive purpose; (3) continually assess the International Atomic Energy Agency's (IAEA) capability to implement the JCPOA verification regime, including whether the IAEA has sufficient access to investigate suspicious sites or allegations of covert nuclear-related activities and whether it has the required funding, manpower, and authority to administer such verification regime; and (4) report to Congress on the matters covered by this bill. "Joint Comprehensive Plan of Action" means the Joint Comprehensive Plan of Action, signed at Vienna July 14, 2015, by Iran and China, France, Germany, the Russian Federation, the United Kingdom, and the United States, with the High Representative of the European Union for Foreign Affairs and Security Policy, and all implementing materials and agreements related to the Joint Comprehensive Plan of Action.