A major part of source rocks in the Zagros Fold Belt were deposited during Neocomian time; the lowermost part of the Garau Formation has charged the Early Cretaceous Petroleum System of the Lurestan province. These source rocks are widely distributed in the Lurestan Depression and in the NW part of the Dezful Embayment. The Kabir-Kuh anticline, which is a prominent structure of the Lurestan province, is more than 200 km long, and contains outcrop of the Garau Formation. Natural fracture systems have an important role in increasing of permeability and sometimes porosity of many reservoirs, and are necessary for the primary migration of hydrocarbons from the source rock to the reservoir. We have collected and analyzed field data on fracture set densities andtypes in Garau Formation and in parts of Sarvak Formation which outcrop in the Kabir kuh anticline of Zagros Belt. According to our analyses we have identified 8 fracture sets in 4 fracture systems: 1) a NNE-SSW transverse fracture system (sets A and B), 2) an ESE-WNW longitudinal fracture system (sets C and D), 3) a NE-SW and NNW-SSE oblique fracture system (sets E and F), 4) a SE-NW and ENE-WSW oblique fracture system (sets G and H). The transverse fractures and their orthogonal stylolites are Early Cretaceous to pre-late Miocene in age, while longitudinal and oblique fracture systems have formed since Late Miocene. Some transverse fractures show calcite infillings. We suggest that there have been two phases of counterclockwise rotation in orientation of the stress fields that produced these fractures, 1) a counterclockwise rotation of the stress field between development of non-mineralized fractures and open fractures and 2) a counterclockwise rotation of the stress field between development of the oblique fracture system (sets E and F) and the extension fractures (sets A and B). These rotations in the stress field have probably occurred due to rotation of the Arabian plate during its convergence to the Eurasian plate.