  Let $\Lambda$ be the path algebra of a finite quiver $Q$ over a
finite-dimensional algebra $A$. Then $\Lambda$-modules are identified with
representations of $Q$ over $A$. This yields the notion of monic
representations of $Q$ over $A$. If $Q$ is acyclic, then the
Gorenstein-projective $\m$-modules can be explicitly determined via the monic
representations. As an application, $A$ is self-injective if and only if the
Gorenstein-projective $\m$-modules are exactly the monic representations of $Q$
over $A$.
