Motivation Accurate probabilistic models of sequence evolution are essential for a wide variety of bioinformatics tasks, including sequence alignment and phylogenetic inference. The ability to realistically simulate sequence evolution is also at the core of many benchmarking strategies. Yet, mutational processes have complex context dependencies that remain poorly modeled and understood. Results We introduce EvoLSTM, a recurrent neural network-based evolution simulator that captures mutational context dependencies. EvoLSTM uses a sequence-to-sequence long short-term memory model trained to predict mutation probabilities at each position of a given sequence, taking into consideration the 14 flanking nucleotides. EvoLSTM can realistically simulate mammalian and plant DNA sequence evolution and reveals unexpectedly strong long-range context dependencies in mutation probabilities. EvoLSTM brings modern machine-learning approaches to bear on sequence evolution. It will serve as a useful tool to study and simulate complex mutational processes. Availability and implementation Code and dataset are available at https://github.com/DongjoonLim/EvoLSTM. Supplementary information Supplementary data are available at Bioinformatics online.