The automatic classification of epileptic electroencephalogram (EEG) is significant in the diagnosis and therapy of epilepsy. A classification algorithm for epileptic EEG based on wavelet multiscale analysis and extreme learning machine (ELM) is proposed in this paper. Firstly, wavelet multiscale analysis is applied to the original EEG to extract its sub-bands. Then, two nonlinear methods, i.e. Hurst exponent (Hurst) and sample entropy (SamEn) are used to the feature extraction of EEG and its sub-bands. Finally, ELM algorithm is employed in epileptic EEG classification with the nonlinear features. The proposed method in this paper achieved 99.5% classification accuracy for the discrimination between epileptic ictal and interictal EEG. The result implies that this method has good prospects in the diagnosis and therapy of epilepsy.