Skin cancer, resulting from the uncontrolled proliferation of melanocytes, is prevalent worldwide with an increasing incidence rate. Skin lesion classification plays a vital role in early diagnosis. However, challenges such as class imbalance and limited interpretability persist. This study proposes DualAttnADCNet, a novel deep learning model based on ResNet-50, to address these issues. The model incorporates a dual attention mechanism, combining channel and spatial attention to enhance feature representation, and an attention-based dense classifier (ADC) to improve classification performance, particularly for underrepresented classes. Experiments on the HAM10000 dataset demonstrate that DualAttnADCNet achieves competitive results, with an accuracy of 92.31% and a weighted F1-score of 91.21%, outperforming the baseline ResNet-50 in handling class imbalance. The integration of DualAttn and ADC notably improves the F1-scores of minority classes such as akiec and bcc. Moreover, the model maintains computational efficiency with 4.17 GFLOPs and 86.69 FPS inference speed. This work presents an effective solution for skin lesion classification with potential value in clinical diagnosis.