AbstractA multistart Nelder–Mead neural network algorithm (multi NM-NNA) is presented, the purpose of which is to solve the problem that the existing nonlinear search algorithms are unstable when inversing earthquake source parameters with GPS data. Multi NM-NNA uses the nonuniform sampling strategy to generate the initial starting points to reduce manual intervention, and the Nelder–Mead simplex algorithm is used to optimize the local optimization capability of the NNA. Different GPS stations and fault types are simulated, and the NNA, hybrid particle swarm optimization (PSO)/simplex algorithm [multipeaks particle swarm optimization (MPSO)], and NM-NNA are used to perform earthquake source parameter inversion, respectively. The simulation experiment results show that the calculation precision of the NM-NNA is not affected by the number of stations, and it has better stability in the inversion of different fault types. Compared with the NNA and MPSO, the NM-NNA is more suitable for earthquake source parameter inversion, and the computational efficiency is higher than the NNA. The NNA, MPSO, NM-NNA, and multi NM-NNA are used to invert the earthquake source parameters of the Bodrum–Kos earthquake and carry out the precision estimation of the parameters. Experimental results show that the parameter estimates inverted by the multi NM-NNA are closer to the existing research results and have smaller standard deviation. It is shown that inversion uncertainty of the multi NM-NNA is lower, the calculation results are more stable, and the computational efficiency of the multi NM-NNA is higher than NNA. In the complex and changeable earthquake environment, the multi NM-NNA has greater application potential.