Manual annotation of airway regions in computed tomography images is a time-consuming and expertise-dependent task. Automatic airway segmentation is therefore a prerequisite for enabling rapid bronchoscopic navigation and the clinical deployment of bronchoscopic robotic systems. Although convolutional neural network methods have gained considerable attention in airway segmentation, the unique tree-like structure of airways poses challenges for conventional and deformable convolutions, which often fail to focus on fine airway structures, leading to missed segments and discontinuities. To address this issue, this study proposes a novel tubular feature extraction network, named TfeNet. TfeNet introduces a novel direction-aware convolution operation that first applies spatial rotation transformations to adjust the sampling positions of linear convolution kernels. The deformed kernels are then represented as line segments or polylines in 3D space. Furthermore, a tubular feature fusion module (TFFM) is designed based on asymmetric convolution and residual connection strategies, enhancing the network's focus on subtle airway structures. Extensive experiments conducted on one public dataset and two datasets used in airway segmentation challenges demonstrate that the proposed TfeNet achieves more accuracy and continuous airway structure predictions compared with existing methods. In particular, TfeNet achieves the highest overall score of 94.95% on the current largest airway segmentation dataset, Airway Tree Modeling(ATM22), and demonstrates advanced performance on the lung fibrosis dataset(AIIB23). The code is available at https://github.com/QibiaoWu/TfeNet.