Malignant melanoma of the conjunctiva (CM) is an uncommon but potentially deadly disorder. Many malignancies show an increased activity of the epigenetic modifier enhancer of zeste homolog 2 (EZH2). We studied whether EZH2 is expressed in CM, and whether it may be a target for therapy in this malignancy. Immunohistochemical analysis showed that EZH2 protein expression was absent in normal conjunctival melanocytes and primary acquired melanosis, while EZH2 was highly expressed in 13 (50%) of 26 primary CM and seven (88%) of eight lymph node metastases. Increased expression was positively associated with tumour thickness (p =0.03). Next, we targeted EZH2 with specific inhibitors (GSK503 and UNC1999) or depleted EZH2 by stable shRNA knockdown in three primary CM cell lines. Both pharmacological and genetic inactivation of EZH2 inhibited cell growth and colony formation and influenced EZH2-mediated gene transcription and cell cycle profile in vitro. The tumour suppressor gene p21/CDKN1A was especially upregulated in CM cells after EZH2 knockdown in CM cells. Additionally, the potency of GSK503 against CM cells was monitored in zebrafish xenografts. GSK503 profoundly attenuated tumour growth in CM xenografts at a well-tolerated concentration. Our results indicate that elevated levels of EZH2 are relevant to CM tumourigenesis and progression, and that EZH2 may become a potential therapeutic target for patients with CM. © 2018 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland.