  Let $(\mathcal{A,B})$ be a complete and hereditary cotorsion pair in the
category of left $R$-modules. In this paper, the so-called Gorenstein
projective complexes respect to the cotorsion pair $(\mathcal{A}, \mathcal{B})$
are introduced. We show that these complexes are just the complexes of
Gorenstein projective modules respect to the cotorsion pair $(\mathcal{A},
\mathcal{B})$. As applications, we prove that both Gorenstein projective
modules with respect to cotorsion pairs and Gorenstein projective complexes
with respect to cotorsion pairs possess of stability.
