This is a multi-center (when more than 1 hospital or medical school team work on a medical research study), randomized (the study drug is assigned by chance), double-blind (neither physician nor participant knows the treatment that the participant receives), placebo-controlled (an inactive substance; a pretend treatment [with no drug in it] that is compared in a clinical trial with a drug to test if the drug has a real effect) and parallel-group (each group of participants will be treated at the same time) study. The study will consist of 3 phases; Screening phase (3 weeks), Treatment phase (12 weeks) and Follow-up phase (4 weeks). Each participant will be enrolled in the study for approximately 19 weeks. Participants with active rheumatoid arthritis despite MTX therapy will receive JNJ-38518168, 100 milligram (mg) per day or matching placebo capsules once daily for 12 weeks. Efficacy will be primarily evaluated by change from Baseline in disease activity index score C-reactive protein at Week 12. Participants' safety will be monitored throughout the study.