Filamentous structures play an important role in biological systems. Extracting individual filaments is fundamental for analyzing and quantifying related biological processes. However, segmenting filamentous structures at an instance level is hampered by their complex architecture, uniform appearance, and image quality. In this paper, we introduce an orientation-aware neural network, which contains six orientation-associated branches. Each branch detects filaments with specific range of orientations, thus separating them at junctions, and turning intersections to overpasses. A terminus pairing algorithm is also proposed to regroup filaments from different branches, and achieve individual filaments extraction. We create a synthetic dataset to train our network, and annotate real full resolution microscopy images of microtubules to test our approach. Our experiments have shown that our proposed method outperforms most existing approaches for filaments extraction. We also show that our approach works on other similar structures with a road network dataset.