The Akri-Bijeel area in the NW Zagros fold-and-thrust belt (Kurdistan region of northern Iraq) has been the focus of petroleum exploration, and its subsurface has been drilled extensively. This makes it possible to combine outcrop studies of this mountainous region with subsurface data. The region has five potential or regionally proven source rock units: the Ora Formation (Devonian–Carboniferous), the Baluti Formation (Upper Triassic), the Sargelu and Naokelekan Formations (Middle–Upper Jurassic), and the Chia Gara Formation (Upper Jurassic–Early Cretaceous). The area has a complex tectonic history, and it is therefore not necessarily clear when source rocks may have been active or inactive and therefore their generative potential. This makes basin modeling particularly useful as a tool to evaluate source rock thermal maturity and the timing of hydrocarbon generation and the amounts expelled. PetroMod version 2017 was used to reconstruct 1D burial and thermal history for four wells. The reconstructed burial and thermal history models were then calibrated against porosity, pressure, temperature, and vitrinite reflectance data. The results of constrained models show significant variations in heat flow through time, with high heat flows during Mesozoic rifting followed by low values, with sharp decreases in heat flow since the end of the Miocene. The present-day average geothermal gradient at Akri-Bijeel is low (18°C/km), with an average heat flow of 32 mW/m2. The low heat flow can best be explained by the rapid deposition of a thick, cold Cenozoic sedimentary section, Zagros thrusting and accompanying uplift and exhumation, and the ongoing circulation of cold meteoric waters under hydrodynamic conditions. Thermal maturity modeling reveals that the present-day oil window extends from a depth of 860 m in well Bakrman-1 down to 5090 m in well Bijeel-1. The generation of hydrocarbons in the modeled source rocks (except for the Ora Formation) continued until it was halted by Zagros folding and thrusting in the Miocene, after which generation ceased or became negligible. Models predict that the majority of the oil discovered at Akri-Bijeel was generated by the Sargelu, Naokelekan, and Chia Gara Formations. On the basis of 1D basin modeling, the Paleozoic Ora Formation generated oil during the Early Triassic and is now in the gas window, and Jurassic source rocks generated oil during the Cretaceous. Volumetric calculations for the five source rock formations modeled in the area suggest that around 4.94 billion tons (or 36 billion barrels [bbl]) of petroleum have been expelled and charged to the reservoirs, indicating significant remaining potential for undiscovered resources.