In the diagnosis and life prediction of gas turbine engines, the gas path model plays a crucial role. However, the gas path model of gas turbine engines established by the component method generally has problems such as slow convergence of balance solution, abnormal convergence, and large model error. To address the convergence problem in the balance solution of the gas path model and the large model deviation, the variable specific heat method is first used to establish the gas path model of the gas turbine engine. Then, the Newton-Raphson method is used to solve the balance equation of the model, several reasons for the convergence of the disturbance model are analyzed, and solutions such as adding variable solution domain boundary constraints are proposed for the solution algorithm. Two types of convergence factors are used to accelerate the solution convergence, ultimately achieving a solution success rate of 97%. To address the issue of significant model errors, both the Particle Swarm Optimization (PSO) algorithm and the Simulated Annealing Particle Swarm Optimization (PSO-SA) algorithm were employed for model optimization. A comparative analysis of the results obtained from the PSO and PSO-SA algorithms substantiates that the PSO-SA algorithm exhibits superior convergence properties and enhanced optimization performance. The model’s absolute error was successfully reduced from the initial 7.27% to 1.59%, and the local absolute error was reduced from a maximum of 19% to about 4.6%.