In this paper, we study the propagation property of the transient signals on the microstrip and taper microstrip liner using the method of the wavelet transform. This method has the advantages of fast compulating and localizing the wave form at any time and at any point along the transmission line to zoom compared with the conventional Fourier transform. We give the dispersion of the Gaussian signal and the rectangle pulse signals on the microstrip and the taper microstrip lines. The results can serve as referance in the study of the propagation of the ultra-high-speed and ultra-wide-band transient signals and in the design of MIC and MMIC.