The analysis of pre-epileptic seizure through EEG (electroencephalography) is an important issue for epilepsy diagnosis. Currently, there exist some methods derived from the dynamics to analyse the pre-epileptic EEG data. It is still necessary to create a novel method to better fit and explain the EEG data for making sense of the seizures' predictability. In this paper, a fractal wavelet-based spectral method is proposed and applied to analyse EEG recordings from rat experiments. Three types of patterns are found from the 12 experiments; moreover three typical cases corresponding to the three types of seizures are sorted out and analysed in detail by using the new method. The results indicate that this method can reveal the characteristic signs of an approaching seizure, which includes the emergence of long-range correlation, the decrease of anti-persistence behaviour with time and the decrease of the fractal dimension. The pre-seizure features and their implications are further discussed in the framework of the theory of criticality. We suggest that an epileptic seizure could be considered as a generalized kind of "critical phenomenon", culminating in a large event that is analogous to a kind of "critical point". We also emphasize that epileptic event emergence is a non-repetitive process, so the critical interpretation meets a certain number of cases.