To accurately predict the annulus pressure build-up (APB)during the drilling and production of deepwater oil and gas wells, the paper establishes an improved APB calculation model. The model considers the impacts of nonlinear properties of the material and casing deformation. The nonlinear properties of the material include the variations of thermal expansion coefficient and compression coefficient of fluid with temperature and pressure, and the variations of elastic modulus and thermal expansion coefficient of casing with temperature. The nonlinear function in the model is obtained by interpolation method, and this study also performs experimental verification and error analysis. During calculation, each annulus is segmented in the axial direction, and the variable temperature is loaded in an incremental manner. Through an example, this model is compared with a simplified model that ignores material nonlinearity and casing deformation; additionally, the effects of various nonlinear parameters and variable temperature of wellbore on the prediction results of APB is explored. The results show that compared with the improved model, the error range of the simplified model is 2.51%-26.11%; in deepwater wells with a small range of variable temperature, ignoring material nonlinearity and casing deformation has a small influence on APB; within a large range of variable temperature, the prediction error of APB caused by neglecting material nonlinearity is very significant; the expansion coefficient of fluid has the greatest influence on the prediction result of APB. If the expansion coefficient of fluid is taken as a constant, the error may reach 70%. © 2020, Editorial Office of ACTA PETROLEI SINICA. All right reserved.