In order to solve the performance prediction and design optimization of power amplifiers (PAs), the performance parameters of Gallium Nitride high-electron-mobility transistor (GaN HEMT) PAs at different temperatures are modeled based on the particle swarm optimization–extreme learning machine (PSO-ELM) and extreme learning machine (ELM) in this paper. Then, it can be seen that the prediction accuracy of the PSO-ELM model is superior to that of ELM with a minimum mean square error (MSE) of 0.0006, which indicates the PSO-ELM model has a stronger generalization ability when dealing with the nonlinear relationship between temperature and PA performance. Therefore, this investigation can provide vital theoretical support for the performance optimization of PA design.