Homeowners Flood Insurance Relief Act of 2013 - Amends the National Flood Insurance Act of 1968 to direct the Administrator of the Federal Emergency Management Agency (FEMA) to provide certain policy holders the option of paying their premiums monthly (or annually or in more frequent installments, as under current law).

Declares the maximum annual chargeable premium rate for a property to be the total appraised value of all structures located on it at the time of its purchase by the current owner of the property divided by 30.

Sets forth a ten-year phase-in period for risk premium rate increases resulting from enactment of the Biggert-Waters Flood Insurance Reform Act of 2012, at the rate of 10% for each year following the effective date of such Act.

Directs FEMA to refund or provide credit to insureds for any flood insurance premiums collected in excess of the mandatory phase-in of rates prescribed by this Act.