In this paper, we prove the following Theorem Let Mn+1 be a closed anti invariant minimal submanifold tangent to the structure vector field of Sasakian manifold M2n+1, then (1) If Ricci curvature of M2n+1 is greated than -2 and H1(M n+1 ,R)≠0 , then Mn+1 is unstable. (2) If Ricci curvature of M2n+1 is not greater that -2, then Mn+1 is stable.
