The work presented here aim to analyze approximate entropy (ApEn) of EEG signals and brain bands when subjects are performing various cognitive tasks. A hypothesis test was applied to evaluate the statistical differences between various cognitive tasks. ApEn was calculated onEEG signals, Alpha bands and Gamma band where the Wilcoxon signed-rank test was applied to analyze the statistical differences between each cognitive mental task. Delta, Theta, and Beta bands were analyzed as well but have not been reported because they do not have enough statistical difference. Results reported a statistical difference (p < 0.05) for the EEG signals in 4 out of 10 pairs of mental tasks; while in the Alpha band we have obtained a statistical difference in 7 out of 10 pairs of mental tasks. The results obtained showed that ApEn have higher values than EEG signals with the Alpha band. These results showed that brain signals of the Alpha band are less complex than EEG signals. Our approach reports the analysis of brain signals with the ApEn algorithm to be a useful tool to discriminate cognitive tasks. © 2013 IEEE.