Head Start Improvement Act of 2014 - Amends the Head Start Act to eliminate, beginning on the first fiscal year following this Act's enactment, the formula for allotting Head Start program funds to Head Start agencies.

Directs the Secretary of Health and Human Services (HHS) to allot block grants for prekindergarten programs to states, the District of Columbia, U.S. territories, the Republic of Palau, and each federally recognized Indian tribe on the basis of each jurisdiction's share of children aged five and younger who are from families with incomes below 130% of the poverty level.

Requires the Governor or other chief executive of each grantee to certify that all grant funds will be used to directly or indirectly provide comprehensive education and related services to low-income children and their families.

Requires grantees to: (1) award subgrants to prekindergarten providers of their choosing, (2) establish rules and standards for those subgrantees to follow, and (3) monitor compliance with those rules and standards.

Gives grantees full flexibility to use the grant funds to finance a prekindergarten education provider, service, or program, including to establish a portable voucher system.

Requires grantees to provide matching funds from nonfederal sources equal to 20% of their grant.