Flood Insurance Premium Relief Act of 2013 - States that the flood insurance risk premium rate for property purchased between July 6, 2012, and January 1, 2015, shall, during the 12-month period beginning upon such purchase, be the amount chargeable for such property immediately before its purchase (thus delaying implementation of the rate increase).

Requires phase-in of the rate increase, following expiration of such 12-month period, over a 10-year period, at 10% for each year.

Makes conforming amendments to the National Flood Insurance Act of 1968.