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This paper proposes a neuro-network-based method for model reduction that combines the generalized Hebbian algorithm (GHA) with the Galerkin procedure to perform the dynamic simulation and analysis of nonlinear microelectromechanical systems (MEMS). An unsupervised neural network is adopted to find the principal eigenvectors of a correlation matrix of snapshots. It has been shown that the extensive computer results of the principal component analysis using the neural network of GHA can extract an empirical basis from numerical or experimental data, which can be used to convert the original system into a lumped low-order macromodel. The macromodel can be employed to carry out the dynamic simulation of the original system resulting in a dramatic reduction of computation time while not losing flexibility and accuracy. Compared with other existing model reduction methods for the dynamic simulation of MEMS, the present method does not need to compute the input correlation matrix in advance. It needs only to find very few required basis functions, which can be learned directly from the input data, and this means that the method possesses potential advantages when the measured data are large. The method is evaluated to simulate the pull-in dynamics of a doubly-clamped microbeam subjected to different input voltage spectra of electrostatic actuation. The efficiency and the flexibility of the proposed method are examined by comparing the results with those of the fully meshed finite-difference method.