Flood Victim Premium Relief Act of 2013 - Amends the National Flood Insurance Act of 1968, with respect to adjustments to flood insurance premiums to reflect the current risk of flood, to limit premium rate increases on specified residential property in federally declared major disaster areas.

Requires premium rate increases or new premium rates on such properties which become effective after July 6, 2012, to be phased in over an 8-year period, at the rate of 5% for each of the first 4 years and 20% for each of the last 4s.

Defines such properties as those located within a major disaster area: (1) for which revised or updated flood insurance rate maps become effective during the 2-year period beginning upon the occurrence of the disaster; or (2) that upon enactment of this Act are eligible for preferred risk rate method premiums for flood insurance coverage, or that were eligible for them at any time during the 12-month period ending upon the occurrence of the disaster.

Requires such a property also to be: (1) owned by the same owner who owned the property at the time of the disaster; and (2) the owner's primary residence since the disaster (except for any periods of non-occupancy resulting from it).