Primary open-angle glaucoma (POAG), is a heritable common cause of blindness world-wide. To identify risk loci, we conduct a large multi-ethnic meta-analysis of genome-wide association studies on a total of 34,179 cases and 349,321 controls, identifying 44 previously unreported risk loci and confirming 83 loci that were previously known. The majority of loci have broadly consistent effects across European, Asian and African ancestries. Cross-ancestry data improve fine-mapping of causal variants for several loci. Integration of multiple lines of genetic evidence support the functional relevance of the identified POAG risk loci and highlight potential contributions of several genes to POAG pathogenesis, including SVEP1, RERE, VCAM1, ZNF638, CLIC5, SLC2A12, YAP1, MXRA5, and SMAD6. Several drug compounds targeting POAG risk genes may be potential glaucoma therapeutic candidates.