  In this paper we have investigated some aspects of gradient $\rho$-Einstein
Ricci soliton in a complete Riemannian manifold. First, we have proved that the
compact gradient $\rho$-Einstein soliton is isometric to the Euclidean sphere
by showing that the scalar curvature becomes constant. Second, we have showed
that in a non-compact gradient $\rho$-Einstein soliton satisfying some integral
condition, the scalar curvature vanishes.
