The reconstruction of top-quark pair-production (tbar t) events is a prerequisite for many top-quark measurements. We use a deep neural network, trained with Monte-Carlo simulated events, to reconstruct tbar t decays in the lepton+jets final state. Comparing our approach to a widely-used kinematic fit, we find significant improvements in the correct assignment of jets to the partons from the decay, and we study the reconstruction performance of several kinematic top-quark properties. We document our workflow for the optimisation of the hyperparameters of the deep neural network. This workflow can be followed by experimental collaborations to retrain the network taking into account their detailed detector simulations.