Structural magnetic resonance imaging (sMRI) combined with deep learning has achieved remarkable progress in the prediction and diagnosis of Alzheimer's disease (AD). Existing studies have used CNN and transformer to build a well-performing network, but most of them are based on pretraining or ignoring the asymmetrical character caused by brain disorders. We propose an end-to-end network for the detection of disease-based asymmetric induced by left and right brain atrophy which consist of 3D CNN Encoder and Symmetry Interactive Transformer (SIT). Following the inter-equal grid block fetch operation, the corresponding left and right hemisphere features are aligned and subsequently fed into the SIT for diagnostic analysis. SIT can help the model focus more on the regions of asymmetry caused by structural changes, thus improving diagnostic performance. We evaluated our method based on the ADNI dataset, and the results show that the method achieves better diagnostic accuracy (92.5\%) compared to several CNN methods and CNNs combined with a general transformer. The visualization results show that our network pays more attention in regions of brain atrophy, especially for the asymmetric pathological characteristics induced by AD, demonstrating the interpretability and effectiveness of the method.