Productivity prediction is of great significance to reservoir development optimization. Based on the geological characteristics of carbonate reservoirs and the development characteristics of fractured vertical wells，a unsteady compound productivity model for the fractured-vuggy carbonate reservoirs was established. The Laplace space solution was obtained by Laplace transform，and the production curve was plotted by stehfest numerical inversion. Cases results show that the accuracy of the model was verified by the comparison of the results calculated by the new model with the actual production data. The change trend of dimensionless production curve shows that the fluid flow can be divided into seven stages：linear flow in artificial fracture，transition flow A，linear flow in natural fracture，bilinear flow in natural fracture and artificial frac ture，transition flow B，matrix linear flow and boundary control flow. The analysis results of influencing factors show that the storage ratio has an effect on early and late stage of productivity. The early stage of productivity is lower when the relative storage ratio between natural fractures and artificial fractures is larger. The larger the relative storage ratio between the matrix and the dissolution pore，the smaller the later productivity. While the medium-term productivity is affected by the channeling coefficient. The higher the channeling coefficient，the lower the drop rate of the medium-term productivity.