The propagation of broadband pulse in a medium with electromagnetically induced transparency (EIT) was studied. The results show that if the carrier frequency of pulse is exactly tuned to the center of the transparency window, and the pulse spectrum is broader than transparency window, the pulse is temporally broadened and the delay effect is significant. If the carrier frequency of pulse the is exactly tuned to the region of absorption, and the pulse spectrum is wide with respect to the width of absorption line, the pulse begins to distort after a certain distance and is split into two parts at last. The peak value depends not only on the frequency and intensity of the coupling field, but also on the length of the sample. Under appropriate conditions, strong and time domain narrowed pulse can be obtained in the output light.