Recently, in order to overcome the disadvantages of unimodal brain-imaging modalities such as low signal-to-noise ratio and vulnerability to motion artifact and to improve system performance, a multimodal imaging system (so-called hybrid system) has been emerging as an attractive alternative. In the present study, to meet the increasing demand on a hybrid brain-imaging data, we introduce open access datasets of electroencephalography (EEG) and near-infrared spectroscopy (NIRS) simultaneously measured during various cognitive tasks. The datasets contain BCI data such as motor imagery (MI)-, and mental arithmetic (MA), and word generation (WG)-related brain signals, and cognitive task data such as n-back (NB)-, and discrimination/selection response (DSR)-related brain signals. We provide the reference results of these datasets, which were validated using analysis pipelines widely used in related research fields. In particular, it was confirmed from classification analysis that a hybrid EEG-NIRS system can yield better classification accuracy than each of unimodal brain-imaging systems.