Targeting epigenetic mechanisms has shown promise against several cancers but has so far been unsuccessful against glioblastoma (GBM). Altered histone 3 lysine 4 methylation and increased lysine‐specific histone demethylase 1A (LSD1) expression in GBM tumours nonetheless suggest that epigenetic mechanisms are involved in GBM. We engineered a dual‐action prodrug, which is activated by the high hydrogen peroxide levels associated with GBM cells. This quinone methide phenylaminecyclopropane prodrug releases the LSD1 inhibitor 2‐phenylcyclopropylamine with the glutathione scavenger para‐quinone methide to trigger apoptosis in GBM cells. Quinone methide phenylaminocyclopropane impaired GBM cell behaviours in two‐dimensional and three‐dimensional assays, and triggered cell apoptosis in several primary and immortal GBM cell cultures. These results support our double‐hit hypothesis of potentially targeting LSD1 and quenching glutathione, in order to impair and kill GBM cells but not healthy astrocytes. Our data suggest this strategy is effective at selectively targeting GBM and potentially other types of cancers.