It has been noted that the identification of the time-frequency bins dominated by the contribution from the direct propagation of the target speaker can significantly improve the robustness of the direction-of-arrival estimation. However, the correct extraction of the direct-path sound is challenging especially in adverse environments. In this paper, a U-net based direct-path dominance test method is proposed. Exploiting the efficient segmentation capability of the U-net architecture, the direct-path information can be effectively retrieved from a dedicated multi-task neural network. Moreover, the training and inference of the neural network only need the input of a single microphone, circumventing the problem of array-structure dependence faced by common end-to-end deep learning based methods. Simulations demonstrate that significantly higher estimation accuracy can be achieved in high reverberant and low signal-to-noise ratio environments.