In this paper, we propose a novel data-driven approach for rainfall–runoff modelling, using the long short-term memory (LSTM) network, a special type of recurrent neural network. We show in three different experiments that this network is able to learn to predict the discharge purely from meteorological input parameters (such as precipitation or temperature) as accurately as (or better than) the well-established Sacramento Soil Moisture Accounting model, coupled with the Snow-17 snow model.