Background: Cognitive dysfunction affects up to 70% of people with progressive MS (PMS). It can exert a deleterious effect on activities of daily living, employment and relationships. Preliminary evidence suggests that performance can improve with cognitive rehabilitation (CR) and aerobic exercise (EX), but existing data are predominantly from people with relapsing-remitting MS without cognitive impairment. There is therefore a need to investigate whether this is also the case in people with progressive forms of the disease who have objectively identified cognitive impairment. It is hypothesized that CR and EX are effective treatments for people with PMS who have cognitive impairment, in particular processing speed (PS) deficits, and that a combination of these two treatments is more effective than each individual treatment given alone. We further hypothesize that improvements in PS will be associated with modifications of functional and/or structural plasticity within specific brain networks/regions involved in PS measured with advanced MRI techniques. Methods: This study is a multisite, randomized, double-blinded, sham controlled clinical trial of CR and aerobic exercise. Three hundred and sixty subjects from 11 sites will be randomly assigned into one of four groups: CR plus aerobic exercise; CR plus sham exercise; CR sham plus aerobic exercise and CR sham plus sham exercise. Subjects will participate in the assigned treatments for 12 weeks, twice a week. All subjects will have a cognitive and physical assessment at baseline, 12 weeks and 24 weeks. In an embedded sub-study, approximately 30% of subjects will undergo structural and functional MRI to investigate the neural mechanisms underlying the behavioral response. The primary outcome is the Symbol Digit Modalities Test (SDMT) measuring PS. Secondary outcome measures include: indices of verbal and non-verbal memory, depression, walking speed and a dual cognitive-motor task and MRI. Discussion: The study is being undertaken in 6 countries (11 centres) in multiple languages (English, Italian, Danish, Dutch); with testing material validated and standardized in these languages. The rationale for this approach is to obtain a robustly powered sample size and to demonstrate that these two interventions can be given effectively in multiple countries and in different languages. Trial registration: The trial was registered on September 20th 2018 at www.clinicaltrials.gov having identifier NCT03679468. Registration was performed before recruitment was initiated.