This work aims to establish a classification framework for the diagnosis of mild cognitive impairment (MCI) at different stages (early MCI and late MCI) through direct analysis of resting-state functional magnetic resonance imaging (rs-fMRI) signals and using the accuracy (total correct rate), specificity (correct rate of late MCI) and sensitivity (correct rate of early MCI) to validate its classification performance. All fMR images of subjects were parcellated into 116 regions of interest (ROIs) by applying the Anatomical Automatic Labeling (AAL) template, and the average rs-fMRI signals of each ROI were extracted. The Hilbert-Huang transform (HHT) was introduced into the framework to decompose each rs-fMRI signal into a series of intrinsic mode functions (IMFs) and to analyze these nonstationary and nonlinear time-series from the perspective of multiresolution. After obtaining the instantaneous frequencies and amplitudes of all IMFs of a signal, the Hilbert weighted frequencies (HWFs) were calculated and combined into a vector as the feature of the corresponding ROI. Support Vector Machine (SVM) was implemented to classify MCI at different stages. We used the independent two-sample t-test as the feature selection method and measured the classification performance through the leave-one-out cross-validation (LOOCV) method. Results on 77 early MCI (eMCI) and 64 late MCI (lMCI) with baseline rs-fMRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) yielded 87.94% classification accuracy. Some of the brain regions with significant differences found by previous studies have been confirmed in this work. We found that HWF characteristics exhibited a significant downward trend in all cerebellar regions. The rs-fMRI signals in differential brain regions have not changed completely, but only altered in some narrow frequency bands. The analysis results showed that during the progress of MCI, the main changes of rs-fMRI were concentrated in IMF3, while IMFs with other indexes also contained HWF features with high SVM weights, such as Orbitofrontal superior frontal gyrus in IMF2, Insula in IMF4, and Lobule Ⅲ of vermis in IMF5, indicating that other IMFs provide important information for the diagnosis of MCI as well. This work confirmed the classification ability of HHT-based classification framework in classification of at different stages of MCI. Through the analysis, we found that during the progress of MCI the main changes of rs-fMRI were concentrated in IMF3, and HWF characteristics showed a significant downward trend in all cerebellar regions.