  Extriangulated categories were introduced by Nakaoka and Palu as a
simultaneous generalization of exact categories and triangulated categories. A
notion of proper class in an extriangulated category is defined in this paper.
Let $\mathcal{C}$ be an extriangulated category and $\xi$ a proper class in
$\mathcal{C}$. We prove that $\mathcal{C}$ admits a new extriangulated
structure. This construction gives extriangulated categories which are neither
exact categories nor triangulated categories. Moreover, we introduce and study
$\xi$-Gorenstein projective objects in $\mathcal{C}$ and demonstrate that
$\xi$-Gorenstein projective objects share some basic properties with Gorenstein
projective objects in module categories or in triangulated categories. In
particular, we refine a result of Asadollahi and Salarian [Gorenstein objects
in triangulated categories, J. Algebra 281(2004), 264-286]. As an application,
the $\xi$-$\mathcal{G}$projective model structures on extriangulated categories
are obtained.
