Syntactic processing deficits are highly variable in individuals with primary progressive aphasia. Damage to left inferior frontal cortex has been associated with syntactic deficits in primary progressive aphasia in a number of structural and functional neuroimaging studies. However, a contrasting picture of a broader syntactic network has emerged from neuropsychological studies in other aphasic cohorts, and functional imaging studies in healthy controls. To reconcile these findings, we used functional magnetic resonance imaging to investigate the functional neuroanatomy of syntactic comprehension in 51 individuals with primary progressive aphasia, composed of all clinical variants and a range of degrees of syntactic processing impairment. We used trial-by-trial reaction time as a proxy for syntactic processing load, to determine which regions were modulated by syntactic processing in each patient, and how the set of regions recruited was related to whether syntactic processing was ultimately successful or unsuccessful. Relationships between functional abnormalities and patterns of cortical atrophy were also investigated. We found that the individual degree of syntactic comprehension impairment was predicted by left frontal atrophy, but also by functional disruption of a broader syntactic processing network, comprising left posterior frontal cortex, left posterior temporal cortex, and the left intraparietal sulcus and adjacent regions. These regions were modulated by syntactic processing in healthy controls and in patients with primary progressive aphasia with relatively spared syntax, but they were modulated to a lesser extent or not at all in primary progressive aphasia patients whose syntax was relatively impaired. Our findings suggest that syntactic comprehension deficits in primary progressive aphasia reflect not only structural and functional changes in left frontal cortex, but also disruption of a wider syntactic processing network.