Several lines of evidence demonstrated the deleterious effect of methamphetamine (MA) on neurological and psychological functions. However, recent evidence on the neurological dysfunctions related to cognitive performance and psychosis in MA abusers needs to be elucidated. Therefore, the present study aimed to investigate the neurological functions using EEG measurement during cognitive tests in MA abusers with (MWP) or without (MWOP) psychosis compared to age-matched normal participants. The quantitative EEG (qEEG) was used to reveal the absolute power in 4 brain-wave frequencies including delta, theta, alpha, and beta waves. The results demonstrated poor attention in both groups of MA abusers. The deficit in mental flexibility was observed in MWP. The deficit in inhibition control and working memory were observed in MWOP. The greater delta, alpha and beta brain waves in multiple brain areas were observed in MWP during the resting (eyes-open) state. The greater alpha wave in multiple brain areas of MWP correlated with poor attention. The greater delta wave and lesser beta wave in the frontal brain correlated with poor inhibition and working memory in MWOP respectively. These findings demonstrated the applicability of EEG to determine neurological dysfunction related to cognitive impairments in MA abusers.