We introduce an open access, multimodal neuroimaging dataset comprising simultaneously and independently collected Electroencephalography (EEG) and Magnetic Resonance Imaging (MRI) data from twenty healthy, young male individuals (mean age~=~26 years; SD~=~3.8 years). The dataset adheres to the BIDS standard specification and is structured into two components: 1) EEG data recorded outside the Magnetic Resonance (MR) environment, inside the MR scanner without image collection and during simultaneous functional MRI acquisition (EEG-fMRI) and 2) Functional MRI data acquired with and without simultaneous EEG recording and structural MRI data obtained with and without the participants wearing the EEG cap. EEG data were recorded with an MR-compatible EEG recording system (GES 400 MR, Electrical Geodesics Inc.) using a 32-channel sponge-based EEG cap (Geodesic Sensor Net). Eyes-closed resting-state EEG data were recorded for two minutes in both the outside and inside scanner conditions and for ten minutes during simultaneous EEG-fMRI. Eyes-open resting-state EEG data were recorded for two minutes under each condition. Participants also performed an eyes opening-eyes closure block-design task outside the scanner (two minutes) and during simultaneous EEG-fMRI (four minutes). The EEG data recorded outside the scanner provides a reference signal devoid of MR-related artifacts. The data collected inside the scanner without image acquisition captures the contribution of the ballistocardiographic (BCG) without the gradient artifact, making it suitable for testing and validating BCG artifact correction methods. The EEG-fMRI data is affected by both the gradient and BCG artifacts. Brain images were acquired using a 3T GE MR750-Discovery MR scanner equipped with a 32-channel head coil. Whole-brain functional images were obtained using a GRE-EPI T2* weighted sequence (TR~=~2000~ms, TE~=~40~ms, 35 interleaved axial slices with 4~mm isometric voxels). Structural images were acquired using an SPGR sequence (TR~=~8.1~ms, TE~=~3.2~ms, flip angle~=~12°, 176 sagittal slices with 1~mm isometric voxels). This stands as one of the largest open access EEG-fMRI datasets available, which allows researchers to: 1) Assess the impact of gradient and BCG artifacts on EEG data, 2) Evaluate the effectiveness of novel artifact removal techniques to minimize artifact contribution and preserve EEG signal integrity, 3) Conduct hardware/setup comparison studies, 4) Evaluate the quality of structural and functional MRI data obtained with this particular EEG system, and 5) Implement and validate multimodal integrative analysis approaches on simultaneous EEG-fMRI data.