There are many achievements in the hydrocarbon migration experimental studies in clastic reservoir, while there are few migration experiments reported in the carbonate reservoir simulations realm. This article is a tentative experimental study on hydrocarbon migration and accumulation in the carbonate reservoir, a complex media, including porosity system and fracture system. This microcosmic experiment simulates oil-water displacement with real core model. Plentiful seepage phenomena were observed in the microcosmic experiments. Three pathways found in the plane pathway include parallel pathway, lean-cross pathway and network pathway. Three types of flow were found, continuous flow, sectioning flow and their combination. Three driving fronts were found in experiment, piston front, encircle front and impulsive front. All these vary with many factors such as fluid pressure, oil saturation, fissure configurations and wettability, and these factors affect each other. The result show that the relation between the fluid pressure and volume of flow is complex segmenting correlative, instead of simple normal correlativity like the pipe flow which follows the Darcy laws, so is that of the fluid pressure and the speed of flow. The speed of flow relates to angle and width of fissure. The speed of flow in the wide fissure that has acute angle with pressure grad is higher than that of narrow fissure with high angle with pressure grad.