Gleviceras is an ammonite genus (order Ammonitida) that lived during the Early Jurassic Period, found in Canada, Hungary, Mexico and the United Kingdom.

Gleviceras produced laterally compressed involute shells with a small umbilicus, close spaced sinuous ribbing, and a sharp keel along venter.

The suture is ammonitic with deep narrow complex lobes.

Gleviceras was described by Buckman in 1918 and is included in the Family Oxynoticeratidae and superfamily Psiloceratoidea.

Species include: Gleviceras is closely related to the genera Cheltonia, Hypoxynoticeras, Oxynoticeras, Paracymbites, Paroxynoticeras, Radstockiceras and Slatterites.