National Center for Social Work Research Act of 2004 - Amends the Public Health Service Act to require the Secretary of Health and Human Services to establish the National Center for Social Work Research to conduct, support, and disseminate targeted research on social work methods and outcomes related to problems of significant social concern. Requires the Secretary to appoint a Director of the Center to: (1) promote research and training designed to inform social work practice; (2) provide policy makers with empirically-based research information; and (3) establish research traineeships to address problems of significant social concern. Establishes an advisory council for the Center.