This paper presents a topology-aware learning strategy for volumetric segmentation of intracranial cerebrovascular structures. We propose a multi-task deep CNN along with a topology-aware loss function for this purpose. Along with the main task (i.e. segmentation), we train the model to learn two related auxiliary tasks viz. learning the distance transform for the voxels on the surface of the vascular tree and learning the vessel centerline. This provides additional regularization and allows the encoder to learn higher-level intermediate representations to boost the performance of the main task. We compare the proposed method with six state-of-the-art deep learning-based 3D vessel segmentation methods, by using a public Time-Of-Flight Magnetic Resonance Angiography (TOF-MRA) dataset. Experimental results demonstrate that the proposed method has the best performance in this particular context.