For significant memory concern (SMC) and mild cognitive impairment (MCI), their classification performance is limited by confounding features, diverse imaging protocols, and limited sample size. To address the above limitations, we introduce a dual-modality fused brain connectivity network combining resting-state functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI), and propose three mechanisms in the current graph convolutional network (GCN) to improve classifier performance. First, we introduce a DTI-strength penalty term for constructing functional connectivity networks. Stronger structural connectivity and bigger structural strength diversity between groups provide a higher opportunity for retaining connectivity information. Second, a multi-center attention graph with each node representing a subject is proposed to consider the influence of data source, gender, acquisition equipment, and disease status of those training samples in GCN. The attention mechanism captures their different impacts on edge weights. Third, we propose a multi-channel mechanism to improve filter performance, assigning different filters to features based on feature statistics. Applying those nodes with low-quality features to perform convolution would also deteriorate filter performance. Therefore, we further propose a pooling mechanism, which introduces the disease status information of those training samples to evaluate the quality of nodes. Finally, we obtain the final classification results by inputting the multi-center attention graph into the multi-channel pooling GCN. The proposed method is tested on three datasets (i.e., an ADNI 2 dataset, an ADNI 3 dataset, and an in-house dataset). Experimental results indicate that the proposed method is effective and superior to other related algorithms, with a mean classification accuracy of 93.05% in our binary classification tasks. Our code is available at: https://github.com/Xuegang-S.