All participants received cisplatin 75 mg/m², pemetrexed 500 mg/m², and durvalumab 1125 mg intravenously on day 1 of a 3-weekly schedule for a maximum of six cycles. Change from cisplatin to carboplatin with an area under the curve of 5 was permitted. Durvalumab was continued for a maximum of 12 months. The primary endpoint was progression-free survival at 6 months, measured according to mRECIST for malignant pleural mesothelioma and analysed in the intention-to treat population. Safety analyses included all participants who receive at least one dose of any study drug. 54 patients were eligible and were followed up for a median of 28·2 months (IQR 26·5–30·2). 31 (57%; 95% CI 44–70) of 54 patients were alive and progression-free at 6 months. The most common grade 3–4 adverse events were neutropenia (seven [13%] patients), nausea (six [11%]), and anaemia (four [7%]). A total of 60 serious adverse events occurred in 29 participants, five of which were considered possibly related to durvalumab. Five patients died during the study treatment; none of these five deaths were attributed to study treatment.