This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short-length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.