Humphrey-Hawkins 21st Century Full Employment and Training Act of 2013 - Directs the Secretary of Labor to establish a Full Employment National Trust Fund with two separate accounts for: (1) Employment Opportunity Grants to states, local governments, and Indian tribes for job-creating activities in communities whose economy is not at a level of full employment; and (2) Workforce Investment programs.

Directs the Secretary to convene a national employment conference to bring together leaders of small, medium, and large businesses, labor, government, and other parties to discuss employment, with particular attention to structural unemployment and the plight of disadvantaged youth.

Amends the Workforce Investment Act of 1998 to revise member composition requirements for state and local workforce investment boards to include at least 25% of the chief executive officers of minority-serving, community-based organizations.

Amends the Internal Revenue Code to impose a tax on certain covered securities transactions, payable by trading facilities that deal in such transactions.