Logopenic progressive aphasia (LPA) is defined clinically by impairments of naming and sentence repetition. The relationship between these impairments and their neural basis has, however, not yet been determined. We aimed to localize cortical thinning associated with naming and repetition deficits using cortical thickness measurements. Consecutive LPA cases (n = 15) were matched with healthy controls (n = 16). All LPA cases underwent general cognitive testing and language assessment using the progressive aphasia language scale. Word retrieval and verbal short-term memory, the core cognitive processes involved in LPA, were assessed using visual confrontation naming and forward digit-span tasks. Cortical thickness was estimated vertex-by-vertex using Freesurfer. The pattern of cortical thinning for the LPA group as well as the location of cortical thinning linked to the impairment of each core cognitive process was estimated using general linear models. LPA cases showed extensive left-sided cortical thinning in which the temporo-parietal junction had the greatest involvement. Impaired naming was associated with cortical thinning of the supramarginal gyrus (BA 40), while reduced digit-span score, regarded as a surrogate marker for sentence repetition, was correlated with thinning of the left superior temporal gyrus (BA 22 and 42). These results suggest that the core manifestations of LPA emerge from the damage to segregated and non-overlapping cortical regions typically affected in this focal presentation of Alzheimer's disease.