Accurate wound segmentation is crucial for the precise diagnosis and treatment of various skin conditions through image analysis. In this paper, we introduce a novel dual attention U-Net model designed for precise wound segmentation. Our proposed architecture integrates two widely used deep learning models, VGG16 and U-Net, incorporating dual attention mechanisms to focus on relevant regions within the wound area. Initially trained on diabetic foot ulcer images, we fine-tuned the model to acute and chronic wound images and conducted a comprehensive comparison with other state-of-the-art models. The results highlight the superior performance of our proposed dual attention model, achieving a Dice coefficient and IoU of 94.1% and 89.3%, respectively, on the test set. This underscores the robustness of our method and its capacity to generalize effectively to new data.