In this paper we show that the projective properties of representations of a quiver $Q={ullet}{ ightarrow}{ullet}{ ightarrow}{ullet}$ as left $R[x]$-modules. We show that if P is a projective left R-module then $0{longrightarrow}0{longrightarrow}P[x]$ is a projective representation of a quiver Q as $R[x]$-modules, but $P[x]{longrightarrow}0{longrightarrow}0$ is not a projective representation of a quiver Q as $R[x]$-modules, if $P{ eq}0$. And we show a representation $0{longrightarrow}P[x]longrightarrow^{id}P[x]$ of a quiver Q is a projective representation, if P is a projective left R-module, but $P[x]longrightarrow^{id}P[x]{longrightarrow}0$ is not a projective representation of a quiver Q as $R[x]$-modules, if $P{ eq}0$. Then we show a representation $P[x]longrightarrow^{id}P[x]longrightarrow^{id}P[x]$ of a quiver Q is a projective representation, if P is a projective left R-module.