In this paper, we prove that on the complete Kahler manifold, if ${ ho}(x){geq}-frac{1}{2}{lambda}_0$ and either ${ ho}(x_0)>-frac{1}{2}{lambda}_0$ at some point $x_0$ or Vol(M)=${infty}$, then the Clifford $L^2$ cohomology group $L^2{mathcal H}^{ast}(M,S)$ is trivial, where $ ho(x)$ is the least eigenvalue of ${mathcal R}_x + ar{{mathcal R}}(x);and;{lambda}_0$ is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M.