The classification of different fine hand movements from electroencephalogram (EEG) signals represents a relevant research challenge, e.g., in BCI applications for motor rehabilitation. Here, we analyzed two different datasets where fine hand movements (touch, grasp, palmar, and lateral grasp) were performed in a self-paced modality. We trained and tested a newly proposed CNN, and we compared its classification performance with two well-established machine learning models, namely, shrinkage-linear discriminant analysis (LDA) and Random Forest (RF). Compared to previous literature, we included neuroscientific evidence, and we trained our Convolutional Neural Network (CNN) model on the so-called movement-related cortical potentials (MRCPs). They are EEG amplitude modulations at low frequencies, i.e., (0.3,3) Hz that have been proved to encode several properties of the movements, e.g., type of grasp, force level, and speed. We showed that CNN achieved good performance in both datasets (accuracy of 0.70±0.11 and 0.64±0.10, for the two datasets, respectively), and they were similar or superior to the baseline models (accuracy of 0.68±0.10 and 0.62±0.07 with sLDA; accuracy of 0.70±0.15 and 0.61±0.07 with RF, with comparable performance in precision and recall). In addition, compared to the baseline, our CNN requires a faster pre-processing procedure, paving the way for its possible use in online BCI applications.