We aimed to investigate functional connectivity and variability across multiple frequency bands in brain networks underlying cognitive deficits in primary-progressive multiple sclerosis (PP-MS) and to explore how they are affected by the presence of cortical lesions (CLs). We analyzed functional connectivity and variability (measured as the standard deviation of BOLD signal amplitude) in resting state networks (RSNs) associated with cognitive deficits in different frequency bands in 25 PP-MS patients (12 M, mean age 50.9 ± 10.5 years) and 20 healthy subjects (9 M, mean age 51.0 ± 9.8 years). We confirmed the presence of a widespread cognitive deterioration in PP-MS patients, with main involvement of visuo-spatial and executive domains. Cognitively impaired patients showed increased variability, reduced synchronicity between networks involved in the control of cognitive macro-domains and hyper-synchronicity limited to the connections between networks functionally more segregated. CL volume was higher in patients with cognitive impairment and was correlated with functional connectivity and variability. We demonstrate, for the first time, that a functional reorganization characterized by hypo-synchronicity of functionally-related/hyper-synchronicity of functionally-segregated large scale networks and an abnormal pattern of neural activity underlie cognitive dysfunction in PP-MS, and that CLs possibly play a role in variability and functional connectivity abnormalities.