A new type of composite lining structure consisting of segments, steel pipes, and concrete lining can be adopted in the water conveyance tunnel to bear large internal water pressure. However, there is still no effective analysis model and calculation method for the parameter influence effect of this new composite lining. In this paper, the load structure method and the elasticity theory are adopted, the stress analysis model and theoretical calculation method of a new type of composite lining of water conveyance tunnel are given, and the influence law of lining structure parameters is studied. Each part of the shield assembled lining is regarded as a stressed spring, and a formula for calculating the equivalent elastic modulus of the overall structure at the joint of the lining under partial tension and partial compression is given. The stress and deformation of each layer of lining are deduced based on the theory of thick-walled cylinders. According to the actual project, the rationality of the calculation method is verified by comparing the results of finite element analysis, and the influence of the thickness of intermediate concrete lining and inner lining parameters on the distribution of force transmission among lining layers is further analyzed. The results show that the radial displacement and circumferential stress of each layer of lining structure decrease with increasing the thickness of the concrete lining. The larger the elastic modulus of the inner lining material is, the smaller the radial displacement of each lining structure will be, but the circumferential stress of the inner lining will increase. In addition, when the thickness of the steel pipe lining is reduced or the internal water pressure is increased, the circumferential stress and radial displacement generated by the inner lining will increase. This analysis model and method considering the deformation coordination relationship solves the problem of setting the parameters of the lining structure and has obvious advantages in the calculation of the stress and deformation of the new composite lining water conveyance tunnel structure, which can provide a theoretical basis for related engineering design.