To accurately master the thermal–hydraulic and stress-field characteristics of the steam generator under the typical operating conditions of high-temperature gas-cooled reactor (HTGR) and to formulate a practical strategy for the safe operation of the steam generator, a numerical simulation program for the three-dimensional flow and heat transfer of the HTGR steam generator has been developed, and a temperature-stress coupling calculation for the helical heat transfer tube has been performed. The porous medium method is used to simplify the complex helical tube structure in the heat transfer region. A mathematical-physical model of the heat transfer characteristics of the shell-side high-temperature helium flow was constructed and an analytical model of the boiling heat transfer characteristics of the tube-side homogeneous flow of water and steam was established. A source term was established to realize the coupled heat transfer calculations of the shell and the tube, and the resulting temperature field of the spiral tube is imported into the finite element software to calculate and analyze the stresses. The results show that the helium and steam outlet temperatures calculated by the program are in good agreement with the design value, and can effectively predict the flow and heat transfer characteristics of the steam generator, the maximum stress of the helical heat transfer tube under the steady state rated power is 255.5Mpa, and the maximum deformation is 2.57 mm. The research in this paper has certain reference value for the design and safe operation of the helical tube steam generator.