Brain-computer interfaces (BCIs) have been widely employed to identify and estimate a user's intention to trigger a robotic device by decoding motor imagery (MI) from an electroencephalogram (EEG). However, developing a BCI system driven by MI related to natural hand-grasp tasks is challenging due to its high complexity. Although numerous BCI studies have successfully decoded large body parts, such as the movement intention of both hands, arms, or legs, research on MI decoding of high-level behaviors such as hand grasping is essential to further expand the versatility of MI-based BCIs. In this study, we propose NeuroGrasp, a dual-stage deep learning framework that decodes multiple hand grasping from EEG signals under the MI paradigm. The proposed method effectively uses an EEG and electromyography (EMG)-based learning, such that EEG-based inference at test phase becomes possible. The EMG guidance during model training allows BCIs to predict hand grasp types from EEG signals accurately. Consequently, NeuroGrasp improved classification performance offline, and demonstrated a stable classification performance online. Across 12 subjects, we obtained an average offline classification accuracy of 0.68 (±0.09) in four-grasp-type classifications and 0.86 (±0.04) in two-grasp category classifications. In addition, we obtained an average online classification accuracy of 0.65 (±0.09) and 0.79 (±0.09) across six high-performance subjects. Because the proposed method has demonstrated a stable classification performance when evaluated either online or offline, in the future, we expect that the proposed method could contribute to different BCI applications, including robotic hands or neuroprosthetics for handling everyday objects.