The continuous wavelet transform is a new approach to the problem of time-frequency analysis of signals such as electroencephalogram (EEG) and is a promising method for EEG analysis. However, it requires a convolution integral in the time domain, so the amount of computation is enormous. In this paper, we propose a fast wavelet transform (FWT) that the corrected basic fast algorithm (CBFA) and the fast wavelet transform for high accuracy (FWTH). As a result, our fast wavelet transform can achieve high computation speed and at the same time to improve the computational accuracy. The CBFA uses the mother wavelets whose frequencies are 2 octaves lower than the Nyquist frequency in the basic fast algorithm. The FWT for high accuracy is realized by using upsampling based on a L-Spline interpolation. The experimental results demonstrate advantages of our approach and show its effectiveness for EEG analysis.