SNAP Improvement Act of 2013 - Amends the Food and Nutrition Act of 2008 to make households in which each member receives state assistance under the temporary assistance to needy families program (TANF), the supplemental security income program (SSI), or aid to the aged, blind, or disabled program (AABD) eligible for the supplemental nutrition assistance program (SNAP, formerly the food stamp program). (Current law bases categorical SNAP eligibility upon state benefits received rather than assistance.)

States that any household in which a member receives substantial lottery or gambling winnings shall lose SNAP eligibility immediately upon receipt of such winnings and shall remain ineligible until the household meets the allowable financial resources and income eligibility requirements.

Eliminates: (1) the exclusion of low-income home energy assistance from SNAP household income determinations, (2) bonuses for states that demonstrate high or most improved performance, (3) inflation adjustments for countable financial resources, (4) funding of employment and training programs, (5) the nutrition education grant program, and (6) funding of Workfare administrative expenses.

Amends the American Recovery and Reinvestment Act of 2009 to: (1) terminate upon enactment of this Act or after October 31, 2013, whichever occurs first, the value of SNAP benefits and consolidated block grants for Puerto Rico and American Samoa from being calculated by using 113.6% of the June 2008 value of the thrifty food plan; and (2) permit the Secretary of Agriculture (USDA) to reduce the value of the maximum allotments, minimum allotments, or consolidated block grants for Puerto Rico and American Samoa below the FY2009 level.