In this work, we propose a novel approach to analyze Epileptic EEG signals using wavelet power spectra and functional principal component analysis. Both continuous and discrete wavelet power spectra are considered. By transforming EEG signals into power spectra, we significantly enhance the functionality of random signals, which makes functional principal component analysis be a suitable technique for further extracting key signal features. We have tested our proposed method using a set of publicly available epileptic EEG. The obtained results demonstrate that wavelet power spectra and functional principal component analysis are promising for feature extraction of epileptic EEG, and they may be useful for epilepsy diagnosis problem.