Summary: Let \(A\) be an extension ring of a ring \(B\), that is, \(B\) is a subring of \(A\) with the same identity. We denote by \(\mathcal{P}\left({A, B} \right)\) the category of all the relatively projective modules. For this extension \(B \hookrightarrow A\), we introduce relatively Gorenstein-projective modules. As Gorenstein-projective modules are closely related to projective modules and there are some good results about Gorenstein dimensions, we want to give a similar relationship between relatively Gorenstein-projective modules and relatively projective modules. The main results are: (1) Let \(B \hookrightarrow A\) be an extension of rings with the same identity. Then the category of all the relatively Gorenstein projective modules is relatively resolving. (2) Let \(B \hookrightarrow A\) be an extension of rings with the same identity. If gl.dim \(\left({A, B} \right) \leq n\), then every relatively Gorenstein-projective module is relatively projective, where gl.dim\(\left({A, B} \right)\) represents the supreme of relatively projective dimension of all the \(A\)-modules.