Abstract This study is a 2D basin modeling to determine the petroleum system (i.e. Cretaceous-Neogene play) of the Karanj and Parsi oilfields in the Southern Dezful Embayment, SW Iran. This system is characterized by occurrence of source rocks of Middle Cretaceous, Late Cretaceous and Paleocene to Eocene (Kazhdumi, Pabdeh and Gurpi Formation), reservoirs of Upper Cretaceous and Late Oligocene–Early Miocene (Ilam-Sarvak and Asmari formations), and seals of Paleocene and Miocene (Pabdeh and Gachsaran Formation). Considering temperature, transformation ratio and vitrinite reflectance, the maturity of source rocks (Kazhdumi, Pabdeh and Gurpi Formation) was investigated. A maturity history analysis showed that the maturity of Kazhdumi, Pabdeh and Gurpi Formation started during 70–60 and 4 Ma, respectively. Generation and expulsion of hydrocarbons started ~16 Ma in the Kazhdumi Formation and ~3 Ma in the Pabdeh Formation that continued up to the present. The analysis of the transformation ratio indicates transformation of significant amounts of Kazhdumi source rocks for generating hydrocarbons. Migration of hydrocarbons from the Kazhdumi Formation is mainly vertically upward. From Pabdeh Formation migration is both vertically upward (to the Asmari reservoir) and downwards (to the Ilam-Sarvak reservoir). However, some local traps have formed due to the hydrocarbon accumulation above the faults. Our results reveal that petroleum generation, migration and entrapment occurred at proper timing which facilitated the migration of hydrocarbons and their accumulation in the reservoirs.