Multi-layer neural networks (NNs) are combined with objective functions of matched-field inversion (MFI) to estimate geoacoustic parameters. By adding hidden layers, a radial basis function neural network (RBFNN) is extended to adopt MFI objective functions. Specifically, shallow layers extract frequency features from the hydrophone data, and deep layers perform inverse function approximation and parameter estimation. A hybrid scheme of backpropagation and pseudo-inverse is utilized to update the RBFNN weights using batch processing for fast convergence. The NNs are trained using a large sample set covering the parameter interval. Numerical simulations and the SWellEx-96 experimental data results demonstrate that the proposed NN method achieves inversion performance comparable to the conventional MFI due to utilizing big data and integrating MFI objective functions.