Let Λ be an Artin algebra and mod-(Gprj_-Λ) the category of finitely presented functors over the stable category Gprj_-Λ of finitely generated Gorenstein projective Λ-modules. This paper deals with those algebras Λ in which mod-(Gprj_-Λ) is a semisimple abelian category, and we call G-semisimple algebras. We study some basic properties of such algebras. In particular, it will be observed that the class of G-semisimple algebras contains important classes of algebras, including gentle algebras and more generally quadratic monomial algebras. Next, we construct an epivalence (called representation equivalence in the terminology of Auslander), i.e. a full and dense functor that reflects isomorphisms, from the stable category of Gorenstein projective representations Gprj_(Q,Λ) of a finite acyclic quiver Q to the category of representations rep(Q,Gprj_-Λ) over Gprj_-Λ, provided Λ is a G-semisimple algebra over an algebraic closed field. Using this, we will show that the path algebra ΛQ of the G-semisimple algebra Λ is CM-finite if and only if Q is Dynkin. In the last part, we provide a complete classification of indecomposable Gorenstein projective representations within Gprj(An,Λ) of the linear quiver An over a G-semisimple algebra Λ. We also determine almost split sequences in Gprj(An,Λ) with certain ending terms. We apply these results to obtain insights into the cardinality of the components of the stable Auslander-Reiten quiver Gprj(An,Λ).