Simultaneous collection of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data has become increasingly popular in neuroscientific studies, because it can provide neural information with both high spatial and temporal resolution. In order to maximally utilize the information contained in simultaneous EEG-fMRI recording, many sophisticated multimodal data-mining methods, such as joint ICA, have been developed. However, these methods normally deal with data recorded in one experimental condition, and they cannot effectively extract information on activities that are distinct in two conditions. In this paper, a new data decomposition method called joint common spatial pattern (jCSP) is proposed. Compared with previous methods, the jCSP method exploits inter-conditional difference in the strength of brain source activities to achieve source separation, and is able to uncover the source activities with the strongest discriminative power. A group analysis based on clustering is further proposed to reveal distinctive jCSP patterns at group level. We applied joint CSP to a simultaneous EEG-fMRI dataset collected from 21 subjects under two different resting-state conditions (eyes-closed and eyes-open). Results show a distinct dynamic pattern shared by EEG alpha power and fMRI signal during eyes-open resting-state.