Axial braided C/C composite materials are widely applied in the throat insert of solid rocket motors. It is the key for the development and design of solid rocket motors to characterize accurately the macromechanical properties of the materials. The Jones-Nelson model is employed to characterize the constitutive relation of the axial braided C/C composite material in this paper. The Jones-Nelson model is expanded and modified to characterize the C/C composite under complex load conditions. The typical external load tests were carried out to verify the accuracy. On this basis, the deformation features of the axial braided C/C composite throat insert are investigated during the working process of motors, and the strain of the throat insert during the working process is obtained by FEM. The strain and temperature in the outer surface of the throat insert are measured in the ground test of motors and are compared with the numerical results by FEM to verify the accuracy of the model. The results show that the result calculated based on the modified Jones-Nelson model by FEM is in a good agreement with the test result. It shows that the modified Jones-Nelson model can better describe the constitutive relation of C/C composite materials, and it can be promoted to the engineering application of the throat insert of solid rocket motors.