This thesis presents a data-driven closure model for the variational multiscale method. The model is trained and tested in the context of a turbulent channel flow with Reτ = 180. Focus is on predicting the closure terms of the momentum equations. The model is trained using norms which only take into consideration local flow accuracy. For this reason long term stability is not addressed explicitly and is not the focus of this work. A convolutional neural network is chosen for its ability to efficiently make use of local spatial and temporal data. Different architectures and inputs are considered for the model. The performance is analyzed in an a priori sense by plotting correlations between the predicted closure terms and the exact closure terms. Using integrated forms of the momentum equation as input produces the highest a priori correlations. Taking multiple time steps as input also proves to be important. The model is then integrated into the simulation of a turbulent channel flow. The closure terms produced by the model are more accurate than those of a modern algebraic model. The flow field produced by the model is thus closer to that of the DNS than the flow field of the algebraic model.