The EEG of epileptic patients often contains sharp waveforms called “spikes”, occurring between seizures. Detecting such spikes is crucial for diagnosing epilepsy. In this paper, we develop a convolutional neural network (CNN) for detecting spikes in EEG of epileptic patients in an automated fashion. The CNN has a convolutional architecture with filters of various sizes applied to the input layer, leaky ReLUs as activation functions, and a sigmoid output layer. Balanced mini-batches were applied to handle the imbalance in the data set. Leave-one-patient-out crossvalidation was carried out to test the CNN and benchmark models on EEG data of five epilepsy patients. We achieved 0.947 AUC for the CNN, while the best performing benchmark model, Support Vector Machines with Gaussian kernel, achieved an AUC of 0.912.