We present the Zurich Cognitive Language Processing Corpus (ZuCo), a dataset combining electroencephalography (EEG) and eye-tracking recordings from subjects reading natural sentences. ZuCo includes high-density EEG and eye-tracking data of 12 healthy adult native English speakers, each reading natural English text for 4-6 hours. The recordings span two normal reading tasks and one task-specific reading task, resulting in a dataset that encompasses EEG and eye-tracking data of 21,629 words in 1107 sentences and 154,173 fixations. We believe that this dataset represents a valuable resource for natural language processing (NLP). The EEG and eye-tracking signals lend themselves to train improved machine-learning models for various tasks, in particular for information extraction tasks such as entity and relation extraction and sentiment analysis. Moreover, this dataset is useful for advancing research into the human reading and language understanding process at the level of brain activity and eye-movement.