This Dataset contains the pre-processed EEG recordings gathered from 20 4-month-old and 20 8-month-old participants who took part in a research study aimed at investigating the origins of the neural basis of peripersonal space in human infancy. The Dataset includes only the recordings of the participants included in the final sample and each file contains only the good, artefact-free trials completed by each participant. For each participant, 2 files are available. The first one (in the "mat" folders) is a MatLab matrix of the values of the EEG recording in each condition, channel, and sample recorded. The second one (in the "raw" folder) is a .raw file compatible with EEGLab and FieldTrip.