Dynamic functional connectivity (dFC) analysis using resting-state functional Magnetic Resonance Imaging (rs-fMRI) is currently an advanced technique for capturing the dynamic changes of neural activities in brain disease identification. Most existing dFC modeling methods extract dynamic interaction information by using the sliding window-based correlation, whose performance is very sensitive to window parameters. Because few studies can convincingly identify the optimal combination of window parameters, sliding window-based correlation may not be the optimal way to capture the temporal variability of brain activity. In this paper, we propose a novel adaptive dFC model, aided by a deep spatial-temporal feature fusion method, for mild cognitive impairment (MCI) identification. Specifically, we adopt an adaptive Ultra-weighted-lasso recursive least squares algorithm to estimate the adaptive dFC, which effectively alleviates the problem of parameter optimization. Then, we extract temporal and spatial features from the adaptive dFC. In order to generate coarser multi-domain representations for subsequent classification, the temporal and spatial features are further mapped into comprehensive fused features with a deep feature fusion method. Experimental results show that the classification accuracy of our proposed method is reached to 87.7%, which is at least 5.5% improvement than the state-of-the-art methods. These results elucidate the superiority of the proposed method for MCI classification, indicating its effectiveness in the early identification of brain abnormalities.