Electroencephalogram-based emotion recognition (EEG-ER) has received increasing attention in the fields of health care, affective computing, and brain-computer interface (BCI). However, satisfactory ER performance within a bi-dimensional and non-discrete emotional space using single-trial EEG data remains a challenging task. To address this issue, we propose a three-layer scheme for single-trial EEG-ER. In the first layer, a set of spectral powers of different EEG frequency bands are extracted from multi-channel single-trial EEG signals. In the second layer, the kernel Fisher's discriminant analysis method is applied to further extract features with better discrimination ability from the EEG spectral powers. The feature vector produced by layer 2 is called a kernel Fisher's emotion pattern (KFEP), and is sent into layer 3 for further classification where the proposed imbalanced quasiconformal kernel support vector machine (IQK-SVM) serves as the emotion classifier. The outputs of the three layer EEG-ER system include labels of emotional valence and arousal. Furthermore, to collect effective training and testing datasets for the current EEG-ER system, we also use an emotion-induction paradigm in which a set of pictures selected from the International Affective Picture System (IAPS) are employed as emotion induction stimuli. The performance of the proposed three-layer solution is compared with that of other EEG spectral power-based features and emotion classifiers. Results on 10 healthy participants indicate that the proposed KFEP feature performs better than other spectral power features, and IQK-SVM outperforms traditional SVM in terms of the EEG-ER accuracy. Our findings also show that the proposed EEG-ER scheme achieves the highest classification accuracies of valence (82.68%) and arousal (84.79%) among all testing methods.