Gestational Diabetes Act of 2018 or the GEDI Act This bill amends the Public Health Service Act to direct the Centers for Disease Control and Prevention (CDC) to develop a multisite gestational diabetes research project to expand and enhance surveillance data and public health research on gestational diabetes. The CDC must expand and intensify public health research on gestational diabetes. The CDC must: (1) award grants for demonstration projects to reduce the incidence of gestational diabetes, the recurrence of such disease in subsequent pregnancies, and the development of type 2 diabetes in women with a history of gestational diabetes; and (2) work with state and Indian tribal-based diabetes prevention and control programs assisted by the CDC to encourage postpartum follow-up after gestational diabetes to reduce the incidence of gestational diabetes and its recurrence, the development of type 2 diabetes in at-risk women, and related complications.