In this paper, a coupled system model of partial differential equations (PDEs) concerning pressure, temperature, velocity, and holdup for a gas-oil-water three-phase steady flow in high-temperature-high-pressure (HTHP) wells is presented. A solution framework shared by the basic models is built, making it convenient to perform to solve. An algorithm solution model using the fourth-order Runge-Kutta method is given. Basic data from "X Well" (HTHP well, 7110 m deep, in Sichuan, PRC) is used as a case study for calculations and a sensitivity analysis is performed on the model. Pressure, temperature, velocity, and hold-up curve graphs, along with the depth of the well, are plotted at different depths. A trend and sensitivity analysis are conducted to test the parameter characteristics. In addition, a comparison between the present model and other models is conducted to illustrate the effectiveness of the model and the algorithm. The results provide both technical reliability for well test design in HTHP gas wells and provides a dynamic analysis of production.