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Detailed pulmonary airway segmentation is a clinically important task for endobronchial intervention and treatment of peripheral located lung cancer lesions. Convolutional Neural Networks (CNNs) are promising tools for medical image analysis but have been performing poorly for cases when existing a significant imbalanced feature distribution, which is true for the airway data as the trachea and principal bronchi dominate most of the voxels whereas the lobar bronchi and distal segmental bronchi occupy a small proportion. In this paper, we propose a Differentiable Topology-Preserved Distance Transform (DTPDT) framework to improve the performance of airway segmentation. A Topology-Preserved Surrogate (TPS) learning strategy is first proposed to balance the training progress within-class distribution. Furthermore, a Convolutional Distance Transform (CDT) is designed to identify the breakage phenomenon with superior sensitivity and minimize the variation of the distance map between the predictionand ground-truth. The proposed method is validated with the publically available reference airway segmentation datasets. The detected rate of branch and length on public EXACT'09 and BAS datasets are 82.1%/79.6% and 96.5%/91.5% respectively, demonstrating the reliability and efficiency of the method in terms of improving the topology completeness of the segmentation performance while maintaining the overall topology accuracy.