Buried volcanic systems are being increasingly studied due to their potential for hydrocarbon and geothermal exploration and subsurface storage of fluids such as CO2. Whilst widespread secondary porosity and fracturing increase reservoir potential in volcanic rocks and associated epiclastic deposits, these processes often also compromise seal integrity, leading to hydrocarbon leakage. Volcanism was widespread offshore northwestern New Zealand in the Miocene and petroleum has been discovered in the buried Kora stratovolcano. We analyse the petroleum system in this volcano using basin modelling to better understand controlling factors on the petroleum potential of buried volcanos. We reproduce charge of this accumulation from a marine source rock, the Waipawa Formation. In addition, there is significant potential for gas generation from Late Cretaceous coal measures of the Rakopi Formation. Modelling results are consistent with an effective fluid plumbing system and suggest that good quality connected reservoirs are present. In addition, Cretaceous faults that were reactivated in the Miocene act as migration pathways. However, models also suggest that significant amounts of petroleum have leaked during volcanic activity and related early maturation of source rocks. Models further predict that overburden and seal rock quality remain insufficient to support large petroleum accumulations. Low seal quality is consistent with the observation of high amplitude anomalies in reflection seismic data above the Kora volcano that are likely related to gas charged sediments and gas leakage. The occurrence of leakage is also consistent with extensive fracturing and oil shows in marine deposits overlying the volcano. These results highlight that the potential of buried volcanic systems to store petroleum and other fluids depends to a large extent on their structural evolution and burial history. On a global scale, hydrocarbon and greenhouse gas leakage of volcanos emplaced in petroliferous basins could have been significant in earth history with the potential to influence global climate.