Muglad Basin, one of the interior passive rift basins in Africa, has experienced multi-cycle passive rifting and superimposition evolution, which distinguishes itself from the active rift or single-cycle passive rift or typical multi-cycle superimposed basins. By application of analysis workflows & approaches to the superimposed basins, including the identification of key geological events during the evolutionary processes and stage division of the evolutionary history, the proto-type basins at the key periods were restored. And based on the analysis on the spatiotemporal difference in rifting intensities, superimposition processes & styles, the superimposition types of each depression or sag as well as its accumulation modes of oil & gas were established. Results show that accompanying with the breakup of Gondwana, and evolution of Atlantic Ocean, Indian Ocean and Red Sea surrounding the Africa Plate, Muglad Basin has experienced three evolutionary periods, namely, the deposition period of Abu Gabra Formation (AG Formation for short) in the Early Cretaceous, the deposition period of Darfur Group in the Late Cretaceous, and the deposition period of Tendi Formation in the Cenozoic. The proto-type basin at Early Cretaceous features several separate grabens and half-grabens, which was produced under the extensional environment having a close relationship with the spreading of Atlantic Ocean; the pro-type basin at Late Cretaceous features the successive development of those early grabens and half-grabens, which was produced under the extensional environment having a close relationship with the rapid movement of Indian Plate. And the proto-type basins at the Cenozoic were mainly confined within the grabens and half-grabens in Kaikang Depression, which was largely affected by the opening of Red Sea. According to the different intensities of three-cycle rifting in each depression or sag and the distinctive processes of tectonic subsidence and sediment filling, the superimposition types of three-cycle rifting were divided into three types, namely, the early-developed, the successive and the dynamic. And the early-developed sag could be represented by the Sufyan Sag, which features the drastically decreasing intensity of three-cycle rifting. In those sags, the amount of basement subsidences and sediment fillings during the first-cycle rifting and post-rifting could account for 79% similar to 82% of the total subsidences and fillings. And the third cycle of rifting and post-rifting was so weak that it was difficult to interpret the layers in seismic section, and even in the logging, it was always omitted. Fula Sag was the most typical sag of the successive. Those sags feature the gradually decreasing intensity of three-cycle rifting & post-rifting. Unlike the former one, the second cycle of rifting & post-rifting still remains quite strong in intensity, which could be proved by the fact the thickness of Darfur Group (Late Cretaceous) in Fula Sag is larger than that of Bentiu Formation (Early Cretaceous) which was deposited during the first cycle of post-rifting. Kaikang Depression was the most typical depression of the dynamic, which features the relatively continuous intensity of the three cycles. When comparing with the formers, every cycle of the three cycles in the Kaikang Depression was larger than any of the early-developed and the successive. Even in the third cycle of rifting & post-rifting, the amount of subsidence and sediment fillings was as much as 2,000m. The spatiotemporal differences in intensities of three-cycle rifting & post rifting determine the differences in petroleum geological conditions for hydrocarbon accumulation and distribution. The dominant play in the early-developed sags is the lower play, and that in the successive sags is the middle play. However, the upper plays were the most dominant plays in those dynamic sags. The study of multi-cycle superimposed passive rift basin in this paper would not only contribute and enrich the research on the structural feature, evolutionary history as well as its effect on the hydrocarbon accumulation of other rift basins in the world, but also had a practical significance in making further strategies for exploration in these basins.