Health Care for the Homeless Act of 1986 - Directs the Secretary of Health and Human Services to make grants to qualified applicant public or private nonprofit entities to enable them to deliver outpatient health care and mental health, case management, and advocacy services to homeless families and individuals. Requires such entities to be qualified recipients of State Medicaid payments under the Social Security Act.

Assigns preference to grant applicants with experience in delivering health care or mental health services to medically underserved populations or to chronically mentally ill individuals. Requires services under such a grant to be provided 24 hours a day. Sets forth other grant requirements. Sets general limitations on charges for such services, except that any services must be provided regardless of the recipient's ability to pay. Sets forth restrictions on the use of grant funds.

Limits any such grant to 75 percent of the cost of services. Outlines application requirements and procedures. Authorizes appropriations for FY 1987.