Urban Jobs Act of 2013 - Amends the Workforce Investment Act of 1998 to authorize the Secretary of Labor to make competitive grants to national or regional private nonprofit community-based organizations to carry out Urban Jobs Programs to provide job training, education, and support services and activities for eligible urban youth to provide them with a pathway to employment, or education leading to employment.

Defines "eligible youth" as individuals ages 18 to 24 who: (1) are not enrolled in secondary or post-secondary school, or (2) are or have been subject to the criminal justice process.

Directs the Secretary to establish a National Jobs Council Advisory Committee.

Expresses the sense of Congress that: (1) community-based affiliates should establish local jobs council advisory committees to aid in establishing local community support for local implementation of the program; and (2) at least one-third of the members of the committee should be employers in high-impact, high-growth industries in the locality.