Contemporary understanding of brain functions provides a way to probe into the mystery of creativity. However, the prior evidence regarding the relationship between creativity and brain wave patterns reveals inconsistent conclusions. One possible reason might be that the means of selecting creative individuals in the past has varied in each study. By distinguishing creative potential as open-ended versus closed-ended based on theoretical views, this study examined different brain wave patterns and cortical control abilities in relation to different creative potentials by using electroencephalogram (EEG) biofeedback equipment. The results demonstrated that participants' performance on the open-ended creative problem was positively related to EEG alpha frequencies, whereas performance on the closed-ended creative problem was related to larger variability in EEG dynamics between alpha and beta waves when performing either open-ended or closed-ended creativity tasks. Further, better control in changing states of brain wave activities according to the EEG biofeedback signals could predict closed-ended creativity performance. Open-ended creativity was related only to the enhancement of alpha signals. These results help clarify previous inconsistent findings, reveal different natures of distinct creativities, and further suggest ways to improve different aspects of creativity with modified biofeedback procedures.