This study is based on the structure of pseudo hyper GR-algebra, analgebra that is partially related on some class of hyper BCI-algebras.This allows us to create a new structure and how this two algebrasare related to each other. A pseudo hyper GR-algebra involves twohyper operations and a set of axioms that come in pairs or a combina-tion of both making it interesting like some algebras established. Thispaper focuses on some properties of pseudo hyper GR-algebras and itsideals. Moreover, pseudo hyper GR-ideals were dened and classied todetermine their relationship to each other.