Aiming to differentiate between MCI patients and elderly control subjects, this study proposes an integrated framework based on spectral-temporal analysis for the automatic analysis of resting-state EEG recordings. This framework firstly eliminates noise employing stationary wavelet transformation (SWT). Then, a set of features is extracted through spectral-temporal analysis. Next, a new wrapper algorithm, named three-dimensional (3-D) evaluation algorithm, is proposed to derive an optimal feature subset. Finally, the Support Vector Machine (SVM) algorithm is adopted to identify MCI patients on the optimal feature subset. Decision tree and K-Nearest Neighbors (KNN) algorithms are also used to test the effectiveness of the selected feature subset. Twenty-two subjects are involved in experiments, of which eleven persons were in an MCI condition and the rest were elderly control subjects. Extensive experiments show that our method is able to classify MCI patients and elderly control subjects automatically and effectively, with the accuracy of 96.94% achieved by the SVM classifier. Decision Tree and KNN algorithms also achieved superior results based on the optimal feature subset extracted by the proposed framework. This study is conducive to timely diagnosis and intervention for MCI patients, and therefore to delay cognitive decline and dementia onset.