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As we know,a complex P is projective if and only if P is exact with Zn(P)projective in R-Mod for each n∈ Z and any morphismf:P→C is null homotopic for any complex C.In this article,we study the notion of DG-Gorenstein projective com-plexes.We show that a complex G is DG-Gorenstein projective if and only if G is exact with Zn(G)Gorenstein projective in R-Mod for each n∈ Z and any morphism f:G→Q is null homo-topic whenever Q is a DG-projective complex.