Electroencephalogram (EEG)-based emotion recognition has garnered significant attention in brain–computer interface research and healthcare applications. While deep learning models have been extensively studied, most are designed for classification tasks and struggle to accurately predict continuous emotional scores in regression settings. In this paper, we introduce EEG-RegNet, a novel deep neural network tailored for precise emotional score prediction across the continuous valence–arousal–dominance (VAD) space. EEG-RegNet tackles two core challenges: extracting subject-independent, emotion-relevant EEG features and mapping these features to fine-grained, continuous emotional scores. The model leverages 2D convolutional neural networks (CNNs) for spatial feature extraction and a 1D CNN for temporal dynamics, providing robust spatiotemporal modeling. A key innovation is the hybrid loss function, which integrates mean squared error (MSE) and cross-entropy (CE) with a Bernoulli penalty to enhance probability estimation and address sparsity in the emotional space. Extensive experiments on the DEAP dataset show that EEG-RegNet achieves state-of-the-art results in continuous emotional score prediction and attains 95% accuracy in fine-grained emotion classification, highlighting its scalability and precision in emotion recognition.