Objective: The concurrent recording of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) is a technique that has received much attention due to its potential for combined high temporal and spatial resolution. However, the ballistocardiogram (BCG), a large-amplitude artifact caused by cardiac induced movement contaminates the EEG during EEG-fMRI recordings. Removal of BCG in software has generally made use of linear decompositions of the corrupted EEG. This is not ideal as the BCG signal is non-stationary and propagates in a manner which is non-linearly dependent on the electrocardiogram (ECG). In this paper, we present a novel method for BCG artifact suppression using recurrent neural networks (RNNs). Methods: EEG signals were recovered by training RNNs on the nonlinear mappings between ECG and the BCG corrupted EEG. We evaluated our model's performance against the commonly used Optimal Basis Set (OBS) method at the level of individual subjects, and investigated generalization across subjects. Results: We show that our algorithm can generate larger average power reduction of the BCG at critical frequencies, while simultaneously improving task relevant EEG based classification. Conclusion: The presented deep learning architecture can be used to reduce BCG related artifacts in EEG-fMRI recordings. Significance: We present a deep learning approach that can be used to suppress the BCG artifact in EEG-fMRI without the use of additional hardware. This method may have scope to be combined with current hardware methods, operate in real-time and be used for direct modeling of the BCG.