Galaxy morphological classification is a fundamental task for understanding galaxy structural evolution and the formation of large-scale cosmic structures. However, large-scale sky survey images often suffer from structural blurring, scale variation, and background interference, posing significant challenges for automated classification. In this study, we propose a deep learning model named AM-GMCNet, which incorporates a center-guided adaptive cropping strategy to significantly improve structural fidelity and feature contrast in galaxy images. In terms of architecture, the model integrates a Convolution-Attention Feature Fusion Module to enhance perception of blurred regions such as spiral arms, and an Adaptive Multi-Scale Fusion Module to unify structural information across different semantic levels, enabling comprehensive representation of complex morphologies. On the five-class classification task of the Galaxy Zoo 2 dataset, the proposed model achieves an accuracy of 96.42%, outperforming a range of mainstream baselines. Further analysis reveals that the model demonstrates an initial capability to capture morphological continuity and evolutionary patterns, particularly in samples with ambiguous structural boundaries, suggesting promising potential for physical interpretability. This work provides a transferable and effective solution for large-scale intelligent recognition and evolutionary analysis of galaxy images.