Global climate models represent small-scale processes, such as clouds and convection, using subgrid models known as parameterizations. Traditional parameterizations are usually based on simplified physical models, and inaccuracies in these parameterizations are a main cause for the large uncertainty in climate projections. One alternative to traditional parameterizations is to use machine learning to learn new parameterizations which are data driven. Attempts to use machine learning for developing new parameterizations for the atmosphere have mainly focused on parameterizing the effects of subgrid processes on thermodynamic and moisture variables, but subgrid momentum transport is also important in simulations of the atmospheric circulation. In this study we use neural networks to develop a parameterization of subgrid momentum transport that learns from coarse-grained output of a high-resolution atmospheric simulation in an idealized aquaplanet domain. We show that substantial subgrid momentum transport occurs due to convection and non-orographic gravity waves. The neural network parameterization we develop has a structure that ensures the conservation of momentum, and it has reasonable skill in predicting momentum fluxes associated with convection. However, the neural network is less accurate for momentum than for energy and moisture, possibly due to the challenging task of predicting momentum fluxes associated with gravity waves, and the difficulty in predicting the sign of momentum fluxes during convection. When this parameterization is implemented in an atmospheric model at coarse resolution it leads to stable simulations, and some characteristics of the atmospheric circulation improve, while some characteristics are sensitive to the exact model configuration. To investigate how the accuracy of neural network momentum parameterization can be improved, we train neural networks using non-local inputs spanning over 3×3 columns of inputs. We find that including the non-local inputs substantially improves the prediction of subgrid momentum transport compared to a single-column formulation. This shows that a single-column approach might not be ideal for the parameterization problem since certain atmospheric phenomena, such as organized convective systems, can cross multiple grid boxes. Overall, our results show that neural-networks parameterization of momentum transport have the potential to improve the representation of subgrid momentum transport, and they also highlight the difficulty in parameterizing subgrid momentum transport.