Mild cognitive impairment (MCI) has been considered as a transition phase to Alzheimer's disease (AD), and the diagnosis of MCI may help patients to carry out appropriate treatments to delay or even prevent AD. Recent advanced network analysis techniques utilizing resting-state functional Magnetic Resonance Imaging (rs-fMRI) has been widely used to get more comprehensive understanding of neurological disorders at a whole-brain connectivity level. However, how to explore effective brain functional connectivity from fMRI data is still a challenge especially when the ultimate goal is to train classifiers for discriminating patients effectively. In our research, we studied the functional connectivity of the whole brain by calculating Pearson's correlation coefficients based on rs-fMRI data, and proposed a set of novel features by applying Two Sample T-Test on the correlation coefficients matrix to identify the most discriminative correlation coefficients. We trained a L2-regularized Logistic Regression classifier based on the five novel features for the first time and evaluated the classification performance via leave-one-out cross validation. We also iterated 10-fold cross validation ten times in order to evaluate the statistical significance of our method. The experiment result demonstrates that classification accuracy and the area under receiver operating characteristic (ROC) curve in our method are 87.5% and 0.929 respectively, and the statistical results prove that our method is statistically significant better than other three algorithms, which means our method could be meaningful to assist physicians efficiently in "real-world" diagnostic situations.