A traditional model of emotion cannot explain the differences in brain activities between two discrete emotions that are similar in the valence-arousal coordinate space. The current study elicited two positive emotions (amusement and tenderness) and two negative emotions (anger and fear) that are similar in both valence and arousal dimensions to examine the differences in brain activities in these emotional states. Frontal electroencephalographic (EEG) asymmetry and midline power in three bands (theta, alpha and beta) were measured when participants watched affective film excerpts. Significant differences were detected between tenderness and amusement on FP1/FP2 theta asymmetry, F3/F4 theta and alpha asymmetry. Significant differences between anger and fear on FP1/FP2 theta asymmetry and F3/F4 alpha asymmetry were also observed. For midline power, midline theta power could distinguish two negative emotions, while midline alpha and beta power could effectively differentiate two positive emotions. Liking and dominance were also related to EEG features. Stepwise multiple linear regression results revealed that frontal alpha and theta asymmetry could predict the subjective feelings of two positive and two negative emotions in different patterns. The binary classification accuracy, which used EEG frontal asymmetry and midline power as features and support vector machine (SVM) as classifiers, was as high as 64.52% for tenderness and amusement and 78.79% for anger and fear. The classification accuracy was improved after adding these features to other features extracted across the scalp. These findings indicate that frontal EEG asymmetry and midline power might have the potential to recognize discrete emotions that are similar in the valence-arousal coordinate space.