This is an open-label (all people know the identity of the intervention), non-randomized, multi-center and Phase 2 study in adult male participants with advanced metastatic prostate cancer. The study consists of 3 parts: Screening (consists of 14 days before study commences on Day -1); Treatment (consists of 4-week dosing cycles wherein trabectedin will be administered as intravenously at a dose of either 0.58 milligram per square meter [mg/m^2] weekly 3-hour infusion, or 1.5 mg/m^2 or 1.2 mg/m^2 every three weeks 24-hour infusion); and Follow-up (until survival after the first dose of trabectedin). Participants will discontinue study treatment at disease progression or unacceptable toxicity unless, in the Investigator's opinion, it is deemed that the participants will continue to derive benefit from trabectedin. Efficacy will be evaluated primarily through decline in prostate-specific antigen (substance in blood that is measured to check for prostate cancer) after 72 hours of therapy on Day 1. Participants' safety will be monitored throughout the study.