Accurately and robustly estimating the state of deformable linear objects (DLOs), such as ropes and wires, is crucial for DLO manipulation and other applications. However, it remains a challenging open issue due to the high dimensionality of the state space, frequent occlusion, and noises. This paper focuses on learning to robustly estimate the states of DLOs from single-frame point clouds in the presence of occlusions using a data-driven method. We propose a novel two-branch network architecture to exploit global and local information of input point cloud respectively and design a fusion module to effectively leverage both the advantages. Simulation and real-world experimental results demonstrate that our method can generate globally smooth and locally precise DLO state estimation results even with heavily occluded point clouds, which can be directly applied to real-world robotic manipulation of DLOs in 3-D space.