Due to geologic and engineering factors，the number and length of the fracture in the vertical wells is various in simulated reservoir volume. Although many productivity models have been proposed for the vertical wells with branch fractures，they are all special cases of two-branch，four-branch and symmetry multi-branch with infinite flow in fractured wells.Thus their reliabilities cannot be guaranteed. Therefore，a new productivity model of the vertical wells with multiple arbitrary fractures needs to be established. Conformal transformation was applied to calculate the productivity of the vertical wells with multiple fractures under steady state flow pattern. Our model is verified by these existing models. In addition，reservoir permeability，thickness，fluid viscosity，length，conductivity，and branch number of the fractures that affect the productivity of the fractured wells were analyzed through cases. The results show that the new built model matches the commonly used models well at a selected value，so its accuracy can be verified. The productivity of the fractured vertical wells increases with the increase of the fracture length，conductivity or branch number，but its increasing range may decrease with the increase of supply radius or branch number.