We prove that P1

→ P2 is a projective representation of a quiverQ = • → • if and only if P1 and P2 are projective left R-modules, f is an injection, and f(P1) ⊂ P2 is a summand. Then, we generalize the result so that a representation M1 f1 → M2 f2 → ·· · fn−2 → Mn−1 fn−1→ Mn of a quiver Q = • → • → •··· • → • → • is projective representation if and only if each Mi is a projective left R-module and the representation is a direct sum of projective representations. 2000 Mathematics Subject Classification: 16E30, 13C11, 16D80