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In this paper, the application of wavelet transform (WT) and wavelet packet transform (WPT) for ECG signals of atrial fibrillation (AF) is presented. Original ECG signals of AF are de-noised, reconstructed and decomposed by WT and WPT. Entropies of each node of the reconstructed ECG signal of AF are calculated. Based on the best basis method and the MDL (minimum description length) criterion, for the given entropy-'log energy' entropy, the optimal wavelet packet tree of the reconstructed ECG signal of AF is established. Ultimately, the non-terminating and the short-time terminating AF are successfully differentiated via the difference of entropies of two types of AF.