Justice for Former American Hostages in Iran Act of 2013 - Establishes in the Treasury the American Hostages in Iran Compensation Fund for the purpose of making payments to: (1) the Americans held hostage in the U.S. embassy in Tehran, Iran, and in other locations in Iran, from November 3, 1979, to January 20, 1981; and (2) certain family members.

Imposes a surcharge, to be deposited into the Fund, of 30% on any fine or penalty imposed, or settlement entered into, for a violation of any law or regulation for any economic activity regarding Iran that is administered by specified federal departments.

Requires Fund payments of: (1) $150,000 plus $10,000 for each day of captivity first to each living former hostage and then to the estate of each deceased former hostage, and (2) $5,000 to each eligible spouse or child of a former hostage for each day of the such hostage's captivity.

Requires a payment recipient to waive and forever release all existing claims against Iran and the United States arising out of the hostage events.

Directs the Secretary of State to notify each individual qualified to receive a payment of the individual's claim status.

States that: (1) if a claim is denied or approved for less than the full amount, the individual shall be entitled to submit additional information; (2) the Secretary may affirm, modify, or revise the former action; and (3) the Secretary's actions in identifying claimants and in disbursing Fund amounts shall be final on all questions of law and fact, and shall not be subject to review by any other U.S. official, agency, or court.