Cerebrovascular segmentation in time-of-flight magnetic resonance angiography (TOF-MRA) volumes is essential for a variety of diagnostic and analytical applications. However, accurate cerebrovascular segmentation in 3D TOF-MRA is faced with multiple issues, including vast variations in cerebrovascular morphology and intensity, noisy background, and severe class imbalance between foreground cerebral vessels and background. In this work, a 3D adversarial network model called A-SegAN is proposed to segment cerebral vessels in TOF-MRA volumes. The proposed model is composed of a segmentation network A-SegS to predict segmentation maps, and a critic network A-SegC to discriminate predictions from ground truth. Based on this model, the aforementioned issues are addressed by the prevailing visual attention mechanism. First, A-SegS is incorporated with feature-attention blocks to filter out discriminative feature maps, though the cerebrovascular has varied appearances. Second, a hard-example-attention loss is exploited to boost the training of A-SegS on hard samples. Further, A-SegC is combined with an input-attention layer to attach importance to foreground cerebrovascular class. The proposed methods were evaluated on a self-constructed voxel-wise annotated cerebrovascular TOF-MRA segmentation dataset, and experimental results indicate that A-SegAN achieves competitive or better cerebrovascular segmentation results compared to other deep learning methods, effectively alleviating the above issues.