Let k be a commutative ring, let C be a small, k-linear, Hom-finite, locally bounded category, and let B be a k-linear abelian category. We construct a Frobenius exact subcategory GP(GPP (B C )) of the functor category B C , and we show that it is a subcategory of the Gorenstein projective objects GP(B C ) in B C . Furthermore, we obtain criteria for when GP(GPP (B C )) = GP(B C ). We show in examples that this can be used to compute GP(B C ) explicitly.