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Fracture-vuggy oil reservoirs contain micrometer-sized dissolved secondary pores, fractures, and meter-sized karst caves. Generally, the researches on the flow mechanism of fractured-vuggy reservoirs are based on the assumption of karst cave-fracture-matrix triple medium that gives a partial differential equation which the pressure satisfies. This triple medium flow equation lays the basics for the well testing theory of fractured-vuggy reservoirs. However, the triple medium equation cannot reflect the actual existence of the karst cave volume in geology. Recently, we proposed a theory of fracture-cave seepage flow coupled with vug pressure wave which takes the vug size into consideration and thus can better describe the fracture-vuggy reservoirs. On the basis of this theory, this work combines the change of formation pressure with time, Duhamel’s theorem, and well testing theory to obtain the mathematical expression of time-varied bottom hole pressure and flow rate in Laplace space. Then, the dynamic inflow performance relationship (IPR) curve of fractured-vuggy reservoir is obtained by inverse Laplace transformations. This dynamic IPR curve can predict the productivity for fractured-vuggy reservoirs using parameters from well test interpretations of pressure recovery. The correctness of this productivity prediction method is verified by filed fractured-vuggy oil well. This productivity prediction method not only utilizes and expands the application of well test interpretation data but also shortens the test time and reduces test costs, which is important for oil development.