•We investigate the anatomy of the perisylvian language network with deterministic tractography.•Participants with high and average language analytical abilities had their arcuate fasciculus virtually dissected.•Linear discriminant analysis was used to establish the best neuroanatomical predictors of the language skills.•The MD values of the right anterior segment were best at differentiating between the two groups.•We conclude that the right white matter fronto-parietal connectivity is important for superior language learning abilities. Aiming at exploring the brain’s structural organisation underlying successful second language learning, we investigate the anatomy of the perisylvian language network in a group of healthy adults, consisting of participants with high and average language analytical abilities. Utilising deterministic tractography, six tracts per participant (left and right long direct segment, left and right indirect anterior segment and left and right indirect posterior segment) were virtually dissected and measurements pertaining to their microstructural organisation were collected. Our results obtained by means of linear discriminant analysis pointed to mean diffusivity (MD) values of three tracts (right anterior, left long and left anterior segments) as best discriminating between the two groups. By far the highest coefficient was obtained for the MD values of the right anterior segment, pointing to the role of the right white matter fronto-parietal connectivity for superior language learning abilities. The results imply the importance of attentional processes and reasoning abilities for successful L2 acquisition, and support previous findings concerning right-hemispheric involvement in language learning.