This is a Phase III, double blind (neither investigator nor participant knows the treatment received), placebo-controlled (an inactive substance that is compared with the study medication to test whether the study medication has a real effect in clinical study), multicenter, 5-arm (treatment groups) study of golimumab at 2 doses (given with or without MTX over a period of 30 minutes) for at least 48 weeks in patients with active RA despite concurrent MTX therapy. The study consists of a treatment period of golimumab IV infusions (IV Period) which ranges from 48 weeks to approximately 140 weeks, assuming an enrollment period of approximately 92 weeks, and a long-term optional extension period (Extension Study) in which golimumab SC injections will be given for 24 weeks. The end of study will be the time the last participant completes the Week E-40 visit (Extension Study) for safety follow-up assessments. For the IV Period, participants will be randomly assigned to 1 of the 5 treatment groups in a 1:1:1:1:1 ratio (approximately 125 patients per group). At Week 16 and Week 24, joint assessment results will be used to allow participants to enter early escape and dose regimen adjustment, respectively, in a blinded fashion. Treatment will be unblinded after the 48-week database lock and participants will be given the option to participate in the Extension Study and receive SC injections of 50mg golimumab (with or without MTX) every 4 weeks for an additional 24 weeks. Safety will be monitored throughout the study. The entire study duration (IV Period plus Extension Study) for each participant will range from 88 weeks up to 192 weeks, assuming an enrollment period of approximately 92 weeks.