Deep complex oil and gas reservoirs are the future directions of oil and gas exploration. The exploration potential of Paleocene deposits in the Lufeng sag is enormous. However, due to the greater burial depth and complex oil and gas accumulation conditions of the Paleocene, few large-scale reservoirs have been discovered and the next exploration strategy is unclear. In this study, based on the Paleocene geological data of the Southern Lufeng sag, a model of hydrocarbon accumulation based on functional element control is constructed using geostatistical and numerical simulation techniques. The hydrocarbon accumulation elements, thresholds, boundaries and scopes are clarified, and the favorable zones of hydrocarbon accumulation of the lower Enping Formation are predicted using the model of hydrocarbon accumulation based on threshold combination control. The results indicate that the source rock, reservoir, caprock, and low-potential area are the four functional elements controlling hydrocarbon accumulation. Since there are three types of low-potential zones, a total of six accumulation elements are considered to control hydrocarbon accumulation, and the corresponding hydrocarbon accumulation control thresholds are determined by the model of hydrocarbon accumulation according to the controlling effects of these accumulation elements. The predicted Type I favorable zones are located in the eastern part of Lufeng 13 east sub-sag and the northern and southern parts of Lufeng 7 sub-sag; Type II favorable zones are located in the western part and around the Lufeng 13 east sub-sag; Type III favorable zones are adjacent to Type II favorable zones. The hydrocarbon shows are all located in the overlapping zone of five or more accumulation elements.