The abuse of Mitragyna speciosa or commonly known as ketum leaves is widespread across Asian countries. Ketum leaves that were originally used as medicine were abused for the purpose of deluding their minds. As it has intoxicated properties that similar to drugs, EEG signals of ketum users may differ from normal people as the ketum may alter the brain signal and the cognitive state of ketum users may decrease. Therefore, this study was conducted to assess the cognitive state between ketum users and non-ketum users in terms of their relaxation state by using brain signal characteristics. A total of 8 subjects were involved in the experimental session. The 8 subjects were divided into two groups which are 4 subjects were ketum users for at least one year while the other 4 subjects were non-ketum users, had enough sleep for at least 6 hours and had no mental disorders. The EEG data was recorded during awaken relaxed state and was filtered using a notch filter and Independent Component Analysis (ICA) to remove the powerline artefacts, eye blinking and eye movement. Stockwell Transform was used to reduce the amount of the large data and extract useful features from the signal. Student's t-test is performed in order to compute the percentages of the differences between the ketum users and non-ketum users in each brain lobe. Mean of Shannon Entropy, mean of Tsallis Entropy, and mean of Hurst Exponent features used were able to elucidate the differences in brain activities between the two groups investigated.