Graduation Promise Act of 2013 - Authorizes the Secretary of Education to make matching grants to states and, through them, subgrants to local educational agencies (LEAs) for differentiated high school improvement systems targeting support to schools with low student achievement and graduation rates after such schools fail for two consecutive years to make annual measurable growth pursuant to state academic performance standards. Allots grant funds to states pursuant to a formula that favors states with low graduation rates and a high percentage of students attending low-income LEAs.

Requires state grantees to establish comprehensive school performance indicators and minimum annual improvement benchmarks for use, in addition to annual measurable growth indicators, in analyzing school performance and determining the improvement category into which a school is placed.

Directs LEA subgrantees to: (1) categorize each of their schools that fail to make annual measurable growth for two consecutive years as needing targeted intervention, whole school reforms, or replacement; (2) convene a local school improvement team for each of such schools that will use school performance indicators, annual measurable growth indicators, and other relevant data to conduct a school needs assessment and develop a multiyear school improvement plan tailored to the school's need categorization; and (3) support the successful implementation of such plans and district-wide high school improvement strategies.

Authorizes the Secretary to award competitive grants to LEAs, nonprofit organizations, and institutions of higher education to develop and implement, or replicate, effective secondary school models for struggling students and dropouts.