The technique of machine learning has been increasingly applied in numerical weather predictions. The aim of this study is to explore the application of a neural network in data assimilation by making use of the convenience in obtaining the tangent linear and adjoint (TL/AD) of a neural network (NN) and formulating a NN-based four-dimensional variational (4D-Var) DA system. A NN-based shallow water (SW) model is developed in this study. The NN model consists of three layers. The weights and biases in the NN-based SW model are trained with 60 years of hourly ERA5 geopotentials and wind field at 500 hPa as initial conditions and the corresponding 12-h forecasts by Model for Prediction Across Scales (MPAS)-SW, in total of 534,697 sets of samples. The 12-h forecasts from independent dates made by NN-based SW prove to closely emulate the simulations by the actual MPAS-SW model. This study further shows that the TL/AD of an NN model can be easily developed and validated. The ease of obtaining the TL/AD makes NN conveniently applicable in various aspects within a data assimilation (DA) system. To demonstrate such, a continuous 4D-Var DA system is also developed with the forward NN and its adjoint. To demonstrate the functionality of the NN-based 4D-Var DA system, the results from a higher resolution simulation will be treated as observations and assimilated to analyze the low resolution initial conditions. The forecasts starting from the analyzed initial conditions will be compared with those without assimilation to demonstrate improvements.