摘要： Let Q be a finite acyclic quiver, J be an ideal of kQ generated by all arrows in Q, A be a finite-dimensional k-algebra. The category of all finite-dimensional representations of (Q,J^2) over A is denoted by rep(Q,J^2,A). In this talk, we introduced the category r.exact(Q,J^2,A) which is a subcategory of rep(Q,J^2,A) of all relation exact representations. The main result of this paper explicitly describes the Gorenstein-projective representations in rep(Q,J2,A), via the relation exact representations plus an extra condition. As a corollary, A is a self-injective algebra, if and only if the Gorenstein-projective representations are exactly the relation exact representations of (Q,J^2) over A.