Progressive supranuclear palsy (PSP), a rare Parkinsonian disorder, is characterized by problems with movement, balance, and cognition. PSP differs from Alzheimer’s disease (AD) and other diseases, displaying abnormal microtubule-associated protein tau by both neuronal and glial cell pathologies. Genetic contributors may mediate these differences; however, the genetics of PSP remain underexplored. Here we conduct the largest genome-wide association study (GWAS) of PSP which includes 2779 cases (2595 neuropathologically-confirmed) and 5584 controls and identify six independent PSP susceptibility loci with genome-wide significant (P < 5 × 10-8) associations, including five known (MAPT, MOBP, STX6, RUNX2, SLCO1A2) and one novel locus (C4A). Integration with cell type-specific epigenomic annotations reveal an oligodendrocytic signature that might distinguish PSP from AD and Parkinson's disease in subsequent studies. Candidate PSP risk gene prioritization using expression quantitative trait loci (eQTLs) identifies oligodendrocyte-specific effects on gene expression in half of the genome-wide significant loci, and an association with C4A expression in brain tissue, which may be driven by increased C4A copy number. Finally, histological studies demonstrate tau aggregates in oligodendrocytes that colocalize with C4 (complement) deposition. Integrating GWAS with functional studies, epigenomic and eQTL analyses, we identify potential causal roles for variation in MOBP, STX6, RUNX2, SLCO1A2, and C4A in PSP pathogenesis.