The parameters of the heat source model have significant influence on the temperature field and sequentially affect the residual stress field. In this paper, a neural-network programme based on the Levenberg–Marquardt algorithm is developed to predict the parameters of Goldak's double-ellipsoidal heat source model. The analytical solution of the heat conduction equation based on the double-ellipsoidal heat source is obtained by integrating a series of instant point heat sources over the volume of the ellipsoidal heat source. The transient temperature distribution and the sizes of the molten pool are obtained under various welding processes by using the analytical method. Then, a neural-network programme is employed to train and predict the heat source parameters. These results of temperature and molten pool size obtained by the numerical simulation with the predicted heat source parameters are calibrated by the published experimental results. The numerical results show a good agreement with the experimental measurements. Finally, the developed Levenberg–Marquardt neural network is employed to predict the heat source parameters in the multi-pass welding process in the laboratory. By comparing the finite element (FE) numerical results with experimental results, the heat source parameters have been successfully identified in the multi-pass welding process.