Quality Foster Care Services Act of 2014 - Amends title XIX (Medicaid) of the Social Security Act (SSA) to extend medical assistance coverage to therapeutic foster care services.

Requires a qualified therapeutic foster care program to be state-licensed and provide: (1) foster care children under 21 with structured daily activities, including the development of age-appropriate social, communication and behavioral skills, trauma-informed and gender-responsive services, crisis intervention and crisis support services, medication monitoring, counseling, and case management; and (2) foster care parents with specialized training and consultation in the management of children with mental illness, trauma, other emotional or behavioral disorders, medically fragile conditions, or developmental disabilities, and specific additional training on the needs of each child provided such services.