Inclusion Criteria: 1. Japanese aged 20 and over at the time of consent 2. Histologically and/or cytologically confirmed pleural or peritoneal malignant mesothelioma 3. Disease not amenable to curative surgery 4. ECOG Performance status 0-1 5. Progressed after previous receipt of 1-2 prior systemic treatments for advanced disease that included a first-line pemetrexed (or anti-folate)-based regimen in combination with platinum agent. 6. Measurable disease, defined as at least 1 lesion (measurable) that can be accurately assessed at baseline by computed tomography CT or MRI and is suitable for repeated assessment. 7. Adequate bone marrow, hepatic, and renal function Exclusion Criteria: 1. Subjects who failed more than 2 prior systemic treatment regimens for advanced malignant mesothelioma 2. Received any prior mAb against CTLA-4, PD1 or PD-L1 3. History of chronic inflammatory or autoimmune disease. 4. Symptomatic, untreated CNS metastasis. 5. Any serious uncontrolled medical disorder or active infection that would impair the subject's ability to receive investigational product. 6. History of other malignancy. 7. History of diverticulitis, inflammatory bowel disease, sarcoidosis syndrome 8. Currently receiving systemic corticosteroids or other immunosuppressive medications. 9. Vaccinated with live attenuated vaccines within 30 days prior to starting tremelimumab treatment 10. Not recovered from all toxicities associated with prior cancer treatment to acceptable baseline status, or a NCI CTCAE ver.3.0 Grade of 0 or 1