The study is a Phase 2 study with 3 parts. Part A is a randomized, double-blind, placebo-controlled, parallel-group, dose-ranging design, Part B is an optional, open label extension design and Part C is an additional optional extension period with an open-label design(up to approximately 104 weeks). Approximately 125 participants will be randomized to 1 of 4 ixekizumab groups or to placebo (approximately 25 participants per group) in Part A. Participants will be evaluated for treatment efficacy and the primary endpoint will be evaluated at week 12. Between week 20 and week 32, participants with a less than 75% improvement in their Psoriasis Area and Severity Index (PASI) score compared to baseline will be eligible to begin Part B. Participants in Part B will receive subcutaneous (SC) injections of ixekizumab 120 milligrams (mg) every 4 weeks through week 236. Subsequent to an amendment on May 2012, administration changed to 80 mg every 4 weeks through Week 236. Participants in Part C may receive SC injections of ixekizumab 80 mg every 4 weeks for up to an additional 104 weeks through approximately week 340. Participants who complete Part A, Part B, and Part C will have a total study participation of approximately 344 weeks.