In this paper, we have proved that a projectively flat Sasakian manifold is an Einstein manifold. Also, if an Einstein-Sasakian manifold is projectively flat, then it is locally isometric with a unit sphere $S^n(1)$. It has also been proved that if in an Einsten-Sasakian manifold the relation $K(X,Y).P=0$ holds, then it is locally isometric with a unit sphere $S^n(1)$.