This is a randomised, Phase IIb, dose-adaptive, multicentre, double-blind, parallel group, placebo-controlled study with the primary objective to assess the efficacy of GSK3196165, in combination with methotrexate (MTX), in subjects with active moderate severe rheumatoid arthritis (RA) despite treatment with MTX. Approximately 210 subjects will be randomised into the study, following a screening period of up to four weeks. The total treatment period is up to 52 weeks, with a 12-week follow-up period after the last dose (Week 50). Subjects will be randomised (1:1:1:1:1:1) to placebo or one of five subcutaneous (SC) GSK3196165 doses, in combination with MTX (at a weekly dose between 15-25 milligram [mg]), previously received for at least 12 weeks, with a stable and tolerated dose and route of administration for >=4 weeks. Escape therapy is provided at specified timepoints in the protocol for subjects that do not achieve adequate disease improvement.