The aim of this work is to present and evaluate a level-set segmentation approach with vesselness-dependent anisotropic energy weights, which focuses on the exact segmentation of malformed as well as small vessels from time-of-flight (TOF) magnetic resonance angiography (MRA) datasets. In a first step, a vesselness filter is used to calculate the vesselness dataset, which quantifies the likeliness of each voxel to belong to a bright tubular-shaped structure and estimate the corresponding vessel directions from a given TOF dataset. The vesselness and TOF datasets are then combined using fuzzy-logic and used for initialization of a variational level-set method. The proposed level-set model has been extended in a way that the weight of the internal energy is locally adapted based on the vessel direction information. Here, the main idea is to weight the internal energy lower if the gradient direction of the level-set is similar to the direction of the eigenvector extracted by the vesselness filter. Furthermore, an additional vesselness force has been integrated in the level-set formulation. The proposed method was evaluated based on ten TOF MRA datasets from patients with an arteriovenous malformation. Manual segmentations from two observers were available for each dataset and used for quantitative comparison. The evaluation revealed that the proposed method yields significantly better segmentation results than four other state-of-the-art segmentation methods tested. Furthermore, the segmentation results are within the range of the inter-observer variation. In conclusion, the proposed method allows an improved delineation of small vessels, especially of those represented by low intensities and high surface curvatures.