This paper considers measuring brain functional connectivity using mutual information (MI). First, we explain the advantage of MI based analysis over the conventional correlation based analysis. Second, we propose a novel approach for MI estimation by exploiting kernel-based probability density function (pdf) estimation and optimization under the maximum likelihood criteria. Finally, the proposed estimator is applied to true fMRI data obtained from Alzheimers Disease (AD) patients and normal control (NC) subjects. The numerical analysis demonstrates the effectiveness of the proposed approach and shows that the MI based analysis result is consistent with clinical observations.