Slow light of an amplitude-modulated Gaussian (AMG) pulse in cesium vapor is demonstrated and studied, since the appropriate amplitude modulation to a single pulse can enrich its spectrum and even enhance the bandwidth utilization efficiency of the slow light system. In a single- Â¿ type electromagnetically induced transparency (EIT) system, the slowed AMG pulse experiences severe distortion, which is mainly owing to the frequency dependent transmission of medium. Additionally, due to its spectral distribution, the frequency dependent dispersion of the medium causes simultaneous slow and fast light for different spectral components and thus a certain dispersive distortion of the AMG pulse. Further, a post-processing method is proposed to recover the slowed (distorted) pulse, which indicates that, by introducing a linear optical system with desired gain spectrum, the optical pulse can be recovered in an Â¿all-opticalÂ¿ way. Finally, we discuss the limitations of this compensation procedure in detail. Although this method is demonstrated in the cesium vapor using EIT, it is also applicable to a wide range of slow light systems.